Studs make ice a non-issue. Doesn't change snow though. (In fact with studs I aim for icy patches rather than snow)

A fat bike makes ice a lot easier to deal with, if you have a fat bike with studs you're totally set there. It handles a LOT more snow than any other tire - but it's still not perfect. It stops working somewhere in between 6-12 inches, depending on the kind of snow.

In Minnesota, they ride fat bikes on the mountain bike trails in the winter. They usually have to go through and pack it down (with snowshoes, from what I understand) first though, or it won't work.