Years ago I built a wheel with a 700c alloy rim and a coaster brake hub that I had scavenged. I still have that wheel somewhere in the basement. I think they make a narrow chain that fits over the wide teeth on the coaster brake.
Then I made snow tires by putting tiny sheet-metal screws in a set of old tires, only I didn't know how to do it, so I put them in with the points facing out. They were really slow, because they stuck in the asphalt. But they sure didn't slip. You're supposed to put them in with the points facing in so they're more like the studs in o-shoes. Obviously they have to be short enough that they don't penetrate to the inside of the tire, and even then I'd probably grind down the points.
A couple of years ago I saw a brilliant way to stud tires. The guy had taken a timing belt of the right length and put the screws in that. So he could take his regular tires, let some air out, slip the belts over them, and pump the tires back up. This allowed him to ride on a frozen lake after having ridden to it on dry pavement with normal rubber.
I've always avoiding riding in slush because of the salt, but if I did I would go the beater route. Probably highly unlikely you'd be ticketed, but note that it's illegal to have studs on the tires of any vehicle (including bikes) on a roadway in southern Ontario.