I have a fairly swank mountain bike made by "Trek". It cost $800. I ride all year round in an area that has 6 metres (METRES) of snowfall a year so I need a solid bicycle. My Friday gig is way out in the boonies beyond bus lines so I really have no choice but to plow through the winter blizzards.
It's a good physical challenge although I have had some dicey moments re; minus-20 degree whiteouts. I'll can off once a year when during a blizzard whiteout I lose my bearings and can't see the gradient of what I am riding on. It's all just white.
No spiked tyres. Wide spikey pedals are way more important, in my experience. If your feet slip/you have to look down at your pedals, you are already halfway rooted.
Gloves, all of them, are useless after 20 minutes at -20 degrees. I've experimented with the lot. Fuck 'em all. Big clunky mittens are the go.