I don't usually do the Snake River Canyon above Alpine (the famous whitewater section) after September/October, but I recall a conversation with a river ranger who said you could do it all winter long if you really wanted to (just reporting a conversation not a personal; observation). So, November should be fine. I bet Cottonwood rapid would be pretty boney. I think the lakes will also be ice free in part of November if you like to do that. Grand Teton NP closes the Snake to human access for the winter, but I don't know exactly when that begins. Other portions of the Snake (outside GTNP) would be open.