We haven't got much snow but this is how I ride through it. The only thing that gets me is the wind, it snakes around in weird ways along my commute.
Excellent.
I am mostly motivated to ride my bike when the salt and snow is out. It's just satisfying knowing I'm rusting my $150 craislist beater bike rather than my expensive car. It also saves gas money, provides exercise, and is actually less stressful.
I wish Cycling was a more common form of transportation for Americans, regardless of location/climate. It would lessen road deterioration, reduce traffic, improve fitness, reduce cost of oil, etc. So many benefits, but it just does not have enough appeal. It does appeal to the greenie advocates, so why not the government push for more cycling?