You can get snow tyres fitted on a bicycle (I had some as a youth) but bicycles are still quite horrible in the winter.

I remember biking home from school during the winter when it was snowing heavily. The sidewalks were completely snowed in with heavy snow so the bike just really went where it wanted to go and very slowly. I eventually decided to move over to the road but I was soon tailgated by a bus. Since the bus was honking at me, I had to pull over to the next bus stop to get him out of my ass. I think it was about at that moment that I decided to ditch winter biking once I could own a car.