When I got my first mountain bike in the 80s, I was thrilled that the 1.75" wide tires would allow riding on snow. The snow-riding experience transformed from "forget it" to "maybe". Those skinny-ish tires did remarkably well so long as one avoided deep snow, ice, or super-slick railroad tracks.
Now I have a Surly Pugsley mountain bike. The tires are 3.7 inches wide. When the tire pressure is down around 25 psi, the tire squishes out and makes a huge contact patch. Snow becomes your friend. The tires are supposed to work on sand, too- but I haven’t made it to Indiana’s beaches for a trial run. That Surly is a special-purpose bike. You wouldn’t want those huge tires every day, on every riding surface.
Instead, you can convert your regular bike into a snow-bike by switching to studded tires. Studded bike tires are available for mountain bikes, hybrid bikes, and road bikes with sufficient clearance. Mountain bikes make the best conversion candidates due to their low center of gravity and predictable steering. The studded tires even do well on ice. Nokian makes the best studded tires (just like automobiles), but there are some other choices as well. You can get 26" or 700c studded tires.
If you really want to ride in snow & ice, go for the studded tires. If you save yourself from one broken collarbone, you’ve paid for the tires.
It’s snowing right now. If I’m lucky, I can be the first rider on the Monon Trail tomorrow morning. There’s some pleasure in laying down 4" wide tire tracks, and imagining joggers wondering "What made those tracks?"