I'll throw in my $0.02 as someone who grew up in Canada and Minnesota, and has since lived in Alaska (albeit the warmer part) as well as one of Colorado's coldest high altitude towns:
Agree with previous suggestions to buy used, and definitely have good snow tires and a block heater. Those items are non-negotiable.
Beyond that, I think you need to consider how you will use the vehicle. Will this just be tooling around Yellowknife to commute and run errands? Or do you plan to get out of town and take it to some more remote areas on a regular basis? This could help you determine small car vs. truck/SUV (i.e., do you need high clearance, true 4WD with hi/lo, or the utility of a truck bed?).
In partial defense of trucks, IME a lot of people in remote, harsh-weather areas prefer trucks not because of their performance driving on snow, but because trucks typically offer other benefits suitable to the area. For example, high clearance and real 4WD may be necessary to access certain homes, ranches, and recreation areas, and the DIY mentality (which is often a necessity in areas like this) frequently puts truck beds to use hauling building materials, firewood, livestock feed, deer/elk, etc.
If I was in your shoes, I would be first deciding whether your driving needs would make a truck or SUV more useful on a regular basis than a compact car, and then go from there to pick a used Toyota model suitable to your needs and budget. There is a reason Toyotas consistently rank among the best in reliability, and command the best resale value of nearly any brand. For specific recommendations: Toyota Corolla with a manual transmission, or look at a 4Runner or Tacoma if you truly need a truck/SUV. Yes, a truck/SUV may be a clown car by MMM standards, but in your particular geographical circumstances such a vehicle might be a good choice.