I have a Krampus, which uses 3" tires, and the main advantage I notice over my old bike is that I have more leeway to lower the tire pressure. Like some people posted above, the worst snow to ride in is the heavy, wet stuff. When it gets right around the freezing point and things are half-melted, I find it almost impossible to keep my front tire from floating all over the place. Drop fifteen degrees from that and the snow starts to get hard and crunchy, making it easier to handle.

With fresh powder I'd say my limit is around four inches. The stuff is so light and fluffy I can just plow through it, but I still have trouble keeping control after a certain point. With more dense snow my limit would be around two inches. A more skilled rider could probably keep control in more snow; after enough practice maybe I'll be there one day. I definitely don't see any bike at all riding through a foot of snow.