For the record, I love my bike and don't own a car. However, the local cycling "activists" in my community are from the same mold as the YIMBY, neoliberal urbanist types. Overwhelmingly white, PMC and childless, who view bicycling and bike infrastructures as the harbinger for livable cites.
When you're a coder or social media marketing douche sitting on an ergonomic chair for 8 hours, cycling for five minutes to and from your loft is an ideal arrangement. However, cycling is a lot less attractive to a blue collar worker who has to travel to a exurb for their grueling 9 hour retail or Amazon warehouse shift standing on their feet. They would much rather nap on the bus after a shift than push pedals for 5 miles.
There is significant research that bike lanes are a trojan horse for gentrification and neoliberal housing development.
In my mid-size city, the twittersphere about local city politics is disproportionately geared towards cycling. It's become a cool kids club for PMCs to get involved in municipal politics, while ignoring much more desperate issues like homelessness and police brutality.
If you can fit some wider studded tires on your bike, and drop the pressure real low it's doable. Studs for the ice and low pressure for the snow. I usually run 15-20PSI on tires that are normally 45-55PSI. Would go lower, but my commute is on the longer side and don't want a pinch flat in the middle of winter.
Fixed gear or single speed can be helpful, with a slight edge towards fixed gear. An iced over derailleur ain't gonna be doing shit anyway. Plus it's one less thing to break when you don't want to be fixing things in sub freezing temps. Fixed is nice because you can start to feel when your tires are slipping through the pedals.
I've found that with a fixed/low psi/studs setup, snow is doable up to 6-7" if fresh and powdery. 3-4" if it's all churned up by cars, and super easy if the road is either a sheet of ice or compacted icy snow of any depth. So not impossible, but certainly way more difficult. I definitely would not recommend it if you hate cold weather, or are not very comfortable on a bicycle.