1. On 32c tires, I can do a 10 mile commute in about 35 minutes. On 38c tires, I can do it in about 45 minutes. I find that anything thinner than 32c just serves to beat me up and not make me go much faster.
2. If I could, I'd go with disc brakes or drum brakes. Having them near the hub makes it harder for snow to get there, and they just stop better anyway. That said, riding in snow, you are experiencing slippery conditions, and having the lock-up potential with something like that might worry me a bit.
3. What kind of heavy snow are we talking about? I once did 10 miles in a blizzard with a 20 mph headwind, and never ever am doing that again. I think it depends on your commute though. If you have a commute that is generally well plowed, flat, and paved, I don't see much of a problem. If you have lots of hills, dirt roads, and 4 foot drifts, yeah, that could suck a lot.
Bottom line for me though is that 20 miles is a fair piece no matter what the conditions - do you want to be out in potentially subzero (Fahrenheit) temperatures for 20 miles?