Actually it may be easier to go about on ice with (appropriate) tires than on your two feet.

I have moved to Vancouver just before I could try to ride my hybrid bike through the winter. I have a few friends who do it, some commuting some kind of long distance, others just having fun riding on the mountain in the snow, and all love it.

Some precautions apply (seeing and being seen etc.) but all in all I think it can be really fun. Check out this web site, I think it's a great resource:
http://www.bikewinter.org/

Enjoy!