There are snow bikes, also called fat bikes, that take 3" wide tires. I think that this is what people use to ride on top of deep snow. I saw one guy in our area commuting on such a bike. While our conditions have not been yet calling for such a bike, the bike was not quite out of line with the surrounding. The guy was actually moving quite fast on top of ice and snow nonuniformities. The latter could have been still coped with using moderate tires, I think 44mm in my case, but slowly compared to that guy.