I'm curious, do you use mountain bike tires to get more traction in the snow, or are you able to use the small, thin street tires so long as the snow is sufficiently slushy/salted/shovelled?
I ride a mountain bike, though my tires are only normal width. I did put studs in my tires to help with icy conditions.[1] So far I've had a good winter of riding.
I don't think anyone would ever ride a road bike in the winter, it would not be possible with the snow the way it is (deep, often drifting, rarely cleared)
Tons of people up here ride "fat tire" winter bikes with up to 4.5 inch tires. They ride the downhill trails right through winter.