The days I was most grateful to have a bicycle, even with a 28 mile one way commute, to ride home in Washington DC were the days it started snowing and the city closed down.
One of those days, I did see 3 collisions between motorist, but I was able to ride in a way that none came near me. There was a five car collision on the highway home, one car flipped upside down. The state troopers closed the highway and motorist got a 2 hour detour. I asked the trooper if I could RIDE through and he said sure. I got home two hours before any of the motorist made it.
As long as it is fresh snow, regular road tires worked fine. Carry a lighter, I had to thaw ice on the large chainring a couple of times. The ice would build up enough to knock the chain off the other chainring.
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Land of the Free, Because of the Brave.