I live in NYC and would like to ride to work during the winter as well. What should one do to a mountain bike? a road bike? If you can also show products that you actually use that would be great.
In the winter you will have to contend with:
1. Ice and snow on the road
This past winter I used the Schwalbe "Marathon Winter" tires for a 3-mile commute along a rural highway and town streets in central Vermont. Our winters are quite a bit more severe than NYC, but if you have ice on the streets that might be unavoidable, studded tires are a must.
At $74 a piece from Peter White Cycles, they aren't cheap, but they are decent in light/thin snow and fabulous on ice. Each tire has 240 tungsten-carbide studs, whose sharp (cylindrical) tips haven't dulled at all for me. While knobby plain-rubber tires will grip alright in snow-on-dry-pavement, as soon as a thin layer of ice forms on top of the pavement (either due to a melt-freeze cycle or packing by auto-tires) the rubber tires will very quickly loose any ability to grip and will send you down hard. With these tires I've had no problem riding a hundred yards on a large patch of black-ice on a fast downhill.
As freiheit mentions, your other big concern is being wet since even if it isn't raining, puddle-splash and lighter mist from passing vehicles will moisten you up. As well, your own tires will throw off a lot of water from wet roads (fenders are very helpful for this).
You have quite a few options to stay dry. Since my commute is only 3 miles, I wear gore-tex rain pants and jacket over my normal work cloths. I also keep a pair of shoes at work and bike in hiking boots during the wet months of October/November and then switch to snow boots January-March.
3. Freezing bike parts
When the air temperature is below freezing and your bike gets covered in moisture you can expect ice to build up. I keep my bike in my warm office at work (on some mats to catch the drips) and in an unheated shed at home. I haven't had repeated problems with freeze-ups, but did have to melt some ice off of the derailleur with a hair drier at home once. If you can get the bike warm at least once a day and keep it stored under a roof you shouldn't have too much build-up. Just remember to test your brakes frequently in case a layer of ice forms on your rims.
4. Cold winds
Due to the speeds of riding, you will almost always have at least 10mph of very cold wind to contend with. Your rain gear will help with that, but you also need to protect:
There are many options for gloves and mittens available, just make sure that you choose something wind-proof and waterproof. For the coldest parts of the winter I use a pair of gore-tex mittens marketed for skiing/snowboarding. I don't find the mittens to get in the way of shifting or braking on my commuter bike, but others prefer gloves for more dexterity.
There are many helmet-liners and covers available to keep your head warm under a bicycle helmet, but I just use a ski helmet (the Giro 9) since it has built-in ear protectors, changeable amounts of ventilation, and nicely fits goggles.
For most of the coldest months I ride with ski goggles. These keep the wind off of my eyes (which otherwise water a lot in the cold wind) and keep most of my face warm. They are also great for protecting the face when it is snowing or sleeting. On a few bitter cold days I've also added neck warmers to cover the lower part of my face, but usually the combination of goggles and the neck of my coat are enough.
Counter-intuitively, my biggest challenge with winter commuting is staying cool. My commute profile is a broad 'w' with downhills at the start each way, a few small hills in the middle, and an uphill at the end. For the first large downhill I try to be a little on the cold side so that I can be comfortable for the rest of the ride. Often though, I bundle up a bit too much and overheat later. The best technique I've found (when riding in work clothes rather than changing) is to layer breathable sweaters or fleece so that I am just short of comfortable out of the wind, then add the wind-proof pants and jacket with the pit-zips and other ventilation open. The wind-proof material will keep most of the wind from cutting through while the ventilation openings will allow enough air circulation to stay cool.
Your area gets colder than mine. I ride through winter, but mostly deal with rain, puddles and cold.
Basics: for wet conditions (puddles, rain), you need fenders (aka mudguards). The fuller the coverage the better, and mudflaps at the end are good. See this comment on the useful accessories community wiki for the specific model I happen to use. You'll also need to rainproof yourself, of course, but fenders will keep the rain from splashing off of the street onto you. Rear fender prevents the stripe up your back, front primarily protects your feet and ankles from splashing. They also protect the bike from that splashing. For my non-icy, non-snowy area, that's all I've equipped my bike with for winter.
For fresh snow or mud, a mountain bike with the kind of knobby tires typical for a mountain bike should be good. On a road bike, you might be able to mount cyclocross tires, but this could prove tricky depending on how much clearance your frame has. However, they probably plow your routes so that you'd hardly ever have to actually ride in snow. (you'll also want fenders for those conditions)
For ice (which can be left behind after plowing), you should look into studded tires. These generally look a lot like the knobby mountain bike tires, but there are metal studs in some of the knobs so that you get a bit of grip on ice. Most studded tires seem to be made for off-road stuff, but there are a few models with a smoother tread designed for use on roads where they might be a patch of ice here or there. You might find some cyclocross type studded tires you could get onto a road bike, but this is likely to be much easier to do on your mountain bike.
Never used any of them, but here's some examples of the more road friendly models of studded tires:
I ride year round, and it can get very cold in January/February. Layers are your friend.
here's my winter riding gear:
The trick is the windproof shell. With that on, it's VERY easy to stay warm, even down to -30˚C or lower. And windproof layers on hands and feet. Wind is evil when it's cold. EVIL!
One trick I use is to put a layer of plastic between the gloves - I wear a thin wool lining glove, and a thicker Sugoi outer glove, and with a layer of plastic sandwiched between them, my fingers stay toasty. Same with feet - plastic between layers of socks.
Also, ski goggles definitely help when it's VERY cold, and when it's snowing a lot.
Of course, with all of the gear on, I look a little strange. But whatever...
And I agree with Adam - once bundled up, the biggest problem is staying cool. That portable sauna heats up fast (especially after a hill or two) and it's hard to cool down through all of those layers :-) It doesn't help when my water bottle freezes solid a few minute from home, either...
When you say plastic, do you mean cling-film, glad wrap, sandwich wrap type stuff?
In Melbourne weather I struggle with the balance between freezing for the first half and melting for the second - does windproof gear breathe properly?
I'd definitely recommend mountain bike style tyres for good grip, and a decent set of mudguards - you don't want to have to wash your bike gear every day.
I rode all year round in Toronto, Ontario, Canada for about 10 years. What I found most useful was warm boots.
I wore winter boots like the ones shown. Though that link is to the -40C version. I also used the -70C version. Which in -35C weather (-31F) are actually quite comfy.
I found that the ankles rotated without a problem, and I could ride in them.
In wet weather, tucking water proof pants over the tops of the boots made for a very comfortable ride.
Please note that the above are intended as a guide for cold weather riding conditions (which are generally dry) and may not work for warmer (above).
Here's a summary of the recommendations on that site:
During freezing winters, I think the most important thing to have is a commando balaclava. I borrowed mine to a friend and it was slow-cold ride without it the next day, actually got cold on that ride. I have used Miltec's commando balaclava and it is warm. You can find a variety of balaclavas here for 5eur. Please, note that you can find this kind of items as Used and very cheap because armies use them, so check your eBay for over-supply baraclava army or something like that, needless to pay for the next-new-sport-wear. Reuse.
I also like to use winter goggles, more here. I have tried a few times with just classes and baraclava but noticed that my eyes become terrible dry/cold/hurting. The specific goggles, more in my reply in the link above, are not traditional skiing goggles. There are many extra good sides such as Reusability and Extendability with additional screens, I don't like skiing-style orangish-or-something-like-that-fixed-things, I have extra lenses for different circumstances that I like to swap. It makes them particularly good for touring because I can carry just one head-thing and all lenses separate. Now during spring and with snow, I use polarized lenses in ESS. When I am in rush, I just pick up old good SWDG because it is easier to switch between the sun-screen and the clear screen -- perhaps a reason why it is still in service. The ESS is better otherwise but switching screens is time-consuming. I am not a racer or anything like that so squeezing few milliseconds with physically attached lenses to the eye-body makes me no difference. I don't know whether the design has contributed to casual skiing goggles but I know the design is outstanding for casual cycling and touring because I don't like to have many skiing goggles, just many screens. Anyway for about 10USD from second-hand over-supply market, I cannot complain.
The only thing I'd add to the other suggestions are mud guards. Good mudguards ("fenders" in the US) are well worth getting to prevent the grime which is generally worse in the wet and nasty conditions.
I personally ride a mountain bike when there is snow or ice because I like having wider tires so all I have to do is be careful on turns when it comes to the slippery stuff. Ironically semi slicks generally haven't caused me a problem. I am used to riding off road though so I can deal with my bike trying to slide out to some extent.
If you're using a road bike a lot I'd recommend full 'sensible' mudguards. i.e. the sort that cover as much of the wheel as possible as opposed to mtb style flaps because as well as preventing you getting mucky they will prevent more of the frame and working components (like chain) from catching so much grime.
With mtb mudguards pay attention to the angles and adjust them as you need to to find what works. If you're leaving it parked in the outside avoid quick release mudguards (unless you want to cart around crud caked bulky parts).
You can also buy extra flaps to extend mudguards.
The only other I would add is very good lights - even during the day.
Having rear flashing lights, and another one higher on your jacket/helmet is a good idea.
Also check that you rear lights / reflectors haven't been covered by thrown up dirt.
I bought (and started to ride) my bike in February this year, in Toronto.
It has fenders and a rack, and bright blinking lights; and I have a pannier, and gloves and a jacket and waistcoat-shaped fleecy, and a hat or helmet.
The LBS I bought it from offers free servicing twice a year for the first two years.
A mountain bike: might you also need to winterize the suspension somehow?
I rode all winter last year in northern Indiana/southern Michigan. My bike is fixed-gear and I notice that the fixed-ness allowed me to control my acceleration and feel the road better, thereby eliminating nearly all slippage.
Lots of good suggestions above.
I'll echo that you definitely need fenders. I recommend them for any commuting bike for any season simply because you'll be miserable riding on wet roads without them.
Of course, nice bright lights are vital. All the really good modern ones are now LED-based. I recommend planet bike super flash for the rear and a good quality front light like something from princeton tec. Lights are not needed to see the road in urban areas but mainly to alert drivers. I find that dawn and dusk are the times when you MOST need lighting, during those times the streetscape lacks contrast and that's when drivers are likely to miss details (like an oncoming cyclist).
Dealing with Corrosion
In the Northeast you'll have to deal with the accumulation of dirt and salt onto your bike. You'll want to get into the habit of wiping/cleaning/lubing the bike more frequently than in the warmer months (not just the chain, but all parts of the bike). Good idea to lube all bearings before the winter and again in the spring (if you're doing serious miles).
Forget any type of "winter cycling gloves" below 40 deg (f). They all suck. Go with ski gloves and you'll be a happy peddler. Also, invest in a good full face balaclava.