As someone who commutes by bike to work in Toronto, (just about everyday in the last 10 years), I've had some experience with snow and cold.
I currently ride an 80's Bianchi, mid-level quality bike, with just enough room for 700x23 tires and narrow fenders, and side pull brakes. Last night was downright fun in a few inches of snow, with slick, narrow tires! Narrow tires cut down through snow to the ground, until the snow gets too deep.
Freewheel pawls freezing open, and the ole 'neutral gear is the worst thing that happens on a road bike. Frozen chain links free up eventually, but pawls require unfreezing. (hot water works, but eventually re-freezes, it's a vicious cycle!)
Ultimately, a fixed gear is the best way to go, it's bulletproof, and gives the option of pedal braking too!
Grant McLean
Toronto, Canada