Thanks, that's what I've found to. Fatbikes are as close to a more stable 3/4 wheel vehicle as you can get on a bike and still ride it through snow (apparently 3/4 wheel bikes are troublesome to try to ride through snow). Skinny tires cut through the snow to the road surface if possible, they're faster and lighter, but don't handle loose snow as well if there's more than several inches of it.

I tried 2" tires a few winters ago by buying a pair, and was very disappointed in them. Seemed like they had all the drawabacks of fat tires (cost, floaty over snow rather than punching through it, heavy and slower) but none of the advantages (not floaty enough to handle more snow, not wide enough to prove more stability when the bike starts to slip). I don't know if there's a niche use for them, but it seemed like the best options were either a 30-40c tire, or jumping up into a full on fatbike.