I'm in Wisconsin and bike all year. I have a hybrid with studded tires (specifically Nokian) and an internal hub. I'd also like to get a fat bike for fresh/powdery snow, but it's rare that's a big deal. There's of course some trade-off between how much traction/stability your tires give you and how much friction & inertia you have to work against when pedaling. Some people have a few different winter options so they can select the bike that will be easiest to propel but still be able to handle the particular day's conditions.

It's good to have warm clothes for your extremities, but your core gets surprisingly warm when you bike with any kind of coat on. I often just wear a think goretex jacket till it's in the single digits fahrenheit. I wear winter boots, warm gloves or mittens (depending on how cold it is), and a balaclava or gaiter. Also ski goggles for really cold/windy weather. If you don't start off feeling somewhat cold, you've overdressed.

I've been biking year-round in Denver for decades. The winters here are relatively mild, but we do get blizzards now and then.

I tried studded tires, but found they didn't help much. Black ice is rare here compared to layers of snow and slush, which don't give studs much to bite into. For me, three inch tires with an open tread pattern at low pressure -- plus an upright riding position that distributes weight evenly between the wheels -- gives me the most confidence.

Regarding the cold, I'd say windproofing is most important, and expedition-style mittens are well worth the investment. You won't need much insulation (except maybe at the extremities) once you start generating body heat. Multiple top layers, each with their own full length zipper, will let you regulate your temperature without getting off the bike. That's especially helpful if you have long climbs and long descents.

I think the main thing is studded tires, and ski jacket. Whitehorse isn't exactly a big town, at most you're 10km from where you want to go, but mostly it's 5km or under. I could follow up and get his exact equipment if you'd like?