Big wheels are best
One thing I found was that big wheels a lot better in snow than small tires. My son and I were going for a spin - he on his 20" 'Tricks" bike and me on a 26" mountain bike. We didn't get very far before he asked to return home to get a 26" middleweight from the garage.
I noticed that 27" work even better unless there is snow-pack or ice underneath. If the surface is icy, the skinny tires are, of course, terrible.
Although I have never seen them, I suspect that knobby 27" tires on an old ten speed might make for a good winter bike (Hmmm....).
In fact, maybe experimenting by making snow tires with an old pair of 27" tires and a fist full of sheet metal screws might be a good holiday project. Hmmm... The risk would be the tire blowing up on you when you put 70 to 90 psi into the tires after perforating them with the screws. I've been around over-inflated tire explosions - scary!
Has anybody tried this?