As others say, the drive itself is not a big deal: ten hours or so including a break for Cheese Whoppers, maybe 11 or 12 if moving slowly over one pass or another. I've tried it on every possible route and found the Coquihalla/Trans Canada fastest from Bellingham, all else being the same. As always in wintertime, take the route with the better weather.
Take seriously: low-temp windshield fluid, winter-weight oil, proper engine coolant mix, strong battery. Block heaters are nice, but I've never had one. Don't be unduly paranoid, but if you have reason to suspect other problems, deal with them: this includes obvious stuff like flushing brake lines that might have water in them and replacing useless donut spares. Throw a warm sleeping bag in the back, and carry drinking water and munchies.
Noted: all of the above applies at least equally to winter driving in, say, Montana.
Hope that helps.