Slick tires, like your conti's, have no problem in wet conditions. If the streets you ride in Boston in winter are just wet with occasional light slush you're fine with what you got.
You'll want knobby tires if you're regularly riding in something soft like dirt, mud, packed snow or very heavy slush. Slick tires are significantly more squirrely in those conditions. In that case, typical cross tires will be better.
Rain and snow aren't so bad. From my experience it's ice, or powder on ice, that can be the real danger. I have Gatorskins, which work just fine in the rain, and for the little amount of snow that I used them in, they weren't too bad. One morning though, the temperature dropped below the dewpoint, and it was below freezing, putting a very thin layer of ice on the road. I took a corner onto a bike path a little too aggressively and took a spill. Luckily no injuries. The bike path had much smoother asphalt than most roads have, adding to the effect of the ice.
Road bikes tires do fine on wet asphalt, because they are thin enough for their load to press away the water underneath. Additional attention should be payed to curbs and gully covers, as they can cause the tire to slip and pulling on the bike. Try to hit each swell as orthogonal as possible both vertical and horizontal to minimize forces.
A road bike’s tyres are very thin and have little tread. A car tyre however is very wide and has a deep tread. You would think that from this that a car tyre would be more suited to gripping the road surface in wet or snowy conditions. However, because the road bike tyre is so thin, it acts like the deep tread and cuts through the water on the road, parting it like Moses (allegedly) parted the Red Sea.
So narrow road tyres, even with only minimal tread can actually be very suited to the rain and snow as long as the road has not iced over.