Having ridden in both Calgary and Edmonton during the winter, I can certainly attest to the fact that "poorly" would be an understatement. They might slog down some of the residential streets once or twice through the winter if they get really bad, but for the most part a lot of the streets around here are simply covered in snow and ice for several months. If you ride outside the confines of core areas, winter tires are almost a necessity here. Edmonton has some particularly entertaining streets I can recall, where they appear to be completely clear until you realize there's a 30 foot frozen puddle underneath a thin layer of surface powder . I used to live on a street in Calgary where there were no visible roads underneath the built up layers of snow and ice, which was constant through all of winter except in the case of a strong chinook (an adiabatic warming wind front). Best yet, some of those strong chinooks would disappear before the water was evaporated, turning entire streets into sheets of ice.

I know some people here who get away without winter tires, but they're core residents whom to my knowledge don't do any riding to other areas of the city.

Essentially you just overcome it with proper equipment and riding technique. Ride through an Albertan winter successfully in the suburbs, and you'll have the skills necessary to really handle some loose terrain next time you're out mountain biking.

Personally, i've used 26x2.1" Schwalbe Ice Spikers, very good for the brutal stuff. 20x1.6" Marathon Winters on my folder, surprisingly good considering the smaller contact patch on those little wheels. This year i'm riding a 700c bicycle, and am going to give the 700x40c Nokian W240s a shot.

My only trouble in winter commuting has been the hands. Some days, gloves and mitts just aren't enough here. I've got a pair of MEC Nanu lobster mitts, which are good to about -20c, but days in December, January and February can easily fall way below that. The eventual solution was to make a pair of pogies, which have now been working great and are comfortable down to -30c. I wear a thinner pair of gloves on top of those so that you have something on your hands while locking up, going inside, etc (which are sweet, because they let me use my touch screen phone while being worn!)