I lived in the Northwest Territories (Canada) and Nunavut for almost 3 decades and used an old hard-tail mountain bike in winter whenever the temperature was bearable (-20 C and above, or even colder on clear sunny days). In my experience, the biggest problem is not the cold or the snow, but the ice. On icy roads or where there is a hard-snowpack, the key to control and traction is the front tire. I have a Schwalbe Ice Spiker 26 x 2.10 with 300 tungsten-carbide spikes (about $100) as my front tire, but in your area, you could do with a cheaper 100 studs. There is no point investing in a studded rear tire. Riding in the lowest gear is also better for traction and control. It is a good idea to replace your brake pads with pads that have curves in them because they are better at scrubing away mud and slush. Also, aluminum rims are better than steel because they don't ice as much. Instead of the usual close-fitting fenders which tend to clog with snow and slush, use those that clip on the down tube and seatpost for more clearance. Also, despite what the "experts" say, WD-40 sprayed liberally on all moving parts (except brakes) as well in all drainage holes and seatpost will be your saviour and will make winter biking a piece of cake. If you have money to spare, you can get bike aerosol lubricant. I never did. Before you use your bike in cold weather, it is also a good idea to repack your bearings. I never did, and my old bike still works...
As I now live in hip Calgary, I now use a single-speed road bike that I bought for $20, with the same 27" tires all year long. Works fine as is without studs.
As for clothing I'd be happy to offer some tips if you wish. Happy riding!