I left Whitehorse in 1983, and back then it had a well developed dealer infrastructure that meant you could own pretty much any mass-market brand and have it serviced easily. Whitehorse is pretty civilized, and even 30 years ago, a FWD car on snow tires easily handled city-based winter driving. It's cold there, but snowfall is less than in many parts of the interior of BC. Where you really want AWD is if you plan on spending time out of town.
My Honda Civic easily got me around town. Lots of people had high-clearance 4X4's but they were mostly for hunting and traveling off highway.
A Subaru would be a pretty awesome compromise, and there is a dealer there. Gasoline used to be heinously expensive compared to down south, but now is comparable to BC prices. $1.30L in Whitehorse now, not much more than many places in Canada, probably less than some, in fact.
It's a great place, btw. Loved living there.