I rode all winter in NoDak for years on a mountain bike, 8 miles/day commuting. The best setup was a wide tire with a relatively high number of knobs of equal sizes inflated to a lower pressure. I can't remember the exact tire but it was made by Specialized and had a very rounded cross section. This worked better than the studded tires I tried.
The freehub would freeze up on really cold mornings (-40f) and the pawls wouldn't engage, so you could pedal but the bike wouldn't move. Fill the freehub with synthetic gear oil and let it drain, then it worked fine.