I bike to work year-round in NYC, and so do many other people. It doesn't actually snow that much, and when it does, it's generally cleared pretty quickly. One thing the city should do to be better on that front is buy some bike-lane-sized snow clearing machines; we currently only have truck-sized snow plows, so the streets are cleared better than the bike lanes.

The biggest problem I have with biking in the winter is when it gets brutally cold, which doesn't happen that often, hardly at all in the past few years. There was this one particularly horrible winter several years back when it was terribly cold for weeks on end, and that was rough.