Can I glue circular pieces of some sort of uneven tiny metal heads, on every other knob of my mountain bike tyre, to bike in winter with snow and ice? If glue sounds too naive to some, there are some really professional hard to undo glues out there today, like those used in contruction work, that are super strong and anti-corrosion and sort of can be molded even and when dried they are like rock.
I am nearly certain the answer is no. Any metal or hard plastic will flex very little compared to the rubber of the tire, which flexes more than you think. There is no glue I have ever heard of or used, including the Gorilla glues and epoxies, that would ever hold these two together - it'd essentially have to be so strong that the rubber won't flex under your weight as you ride, and unless it's top secret I'd just sum it up to be: that doesn't exist and probably never will.
I'd even go further and say even if you got them joined, it wouldn't be a very good or effective tire. If money's really that tight, look for used studded tires on craigslist or eBay - some will be half retail, at least, and may actually help your traction.
Drilling, however, is not hard. You select a screw that protrudes from the lug by the amount you want (1/8" or so for a bicycle would be appropriate), screw it in with a drill from the outside so there's a hole on the inside, then screw it through from the inside out. Then you need to line the inside with rim tape so that the screw heads don't pop your inner tube, but if you do this yourself, they probably will (there aren't enough tire/metal bands like a motorcycle/vehicle tire to keep the screws in place, they'll start pushing into the tube and eventually get through).
In my opinion, neither option is good, or would do anything for your traction besides waste your time.
The problem IMO will be that you need a glue that flexes with the rubber tyre. A rigid glue will just break off taking some of the rubber from the tyre with it. But given a flexible glue that bonds to the rubber and fills the space between tyre and metal object, I think it could work. I'm imagining something like the sealant glues that come in a sealant gun, rather than a cyanoacetate type super glue. The ones used to glue concrete together, for example, that have to fill gaps as well as adhere.
The metal bits will be more of a problem I think. You need a good area for the glue to stick to, but you also need sharp edges to grip the snow. So just attaching 10mm washers flat on the tyre probably won't help. I suspect you'll end up gluing screws across the tyre to more or less match the way the DIY screw tyres work. I suggest covering the screw with glue, then let the glue wear away from the outside when it hits the track. I'd be tempted to start by trying a few screws with each type of glue that I had available just to see whether any of them work at all. And whether you can ride the bike with this setup.
Usual caveats apply: I haven't done this, I doubt it will work, but this seems to be to be the approach least unlikely to fail.
There's a video here of a guy putting studs on ATV tires. They just screw into the tire knobs. I imagine this would be much harder on a bicycle (since the tread is much thinner and you have less room for error) but not impossible.
I would forget about adhesives - you need something that sticks to the tread with just mechanical friction.