I had a bad experience during one of the huge 2010 snowstorms--got stuck on the side of the road for seven hours. Of course, I ran out of gas, and my battery died, and so all I had to keep warm was my suit and overcoat. (I removed the zip-in lining to wrap around my feet. It was bad.) Since then, I've been wary of driving in snow, but the dusting we got last night just wasn't enough to deter me by the time I walked outside this morning and realized, "Hey, it snowed last night."
If you're careful and thorough, and you make sure to wipe/shake/knock the snow off your calfskin shoes, they should be able to hold up. Dry them off at your earliest opportunity. Overshoes or galoshes aren't a bad idea, but make sure they go up high enough, or you'll just end up with snow inside your shoes.
The real problem, though, is the dry air and attendant static electricity. My heavy wool coat actually stuck to my pants leg yesterday (granted, they were tweed pants). Really messes with the "drape" we all prize. A spray bottle of water is a useful fix, but it never works for me past about 15 minutes. I hear hairspray works well, but I hesitate to touch my suits with that.
Anyway, here's to dressing up even when the weather disagrees.