I'm sure not everyone will agree, but I'm going to suggest good mud terrains, and get them siped.
In deep snow, mud terrains rock. I have had excellent results with various mud terrains, aired down (even 10-15psi helps a lot). Not all mud terrains are bad in light snow, I happen to love my BFG KM2s since I have had them. Even with our ice storm last year (over an inch of solid ice) I was able to get everywhere I needed to go, up and down hills, pulling around fallen trees and such. They are the quietest, smoothest mud terrains I have owned. I have over 20k miles on them and they show very little wear. If I lived somewhere with more snow/ice, I would have got them siped in the center tread blocks and I bet they would be amazing.
The BFG a/ts are good tires, but in mud they clog up horribly, and they do not work well in deep snow.
It is a good idea to carry chains either way.