My tires are Schwalbe Marathon Winter 26x1.75.
When there is a lot of snow I wish I had a more aggressive front tire because the MW's don't have a lot of grip on snow.
When the slush turned into ice I wish I had 26x2.0 because the ride is really bumpy.
It's all a compromise what you pick, like previous poster say, it's all a matter of the conditions.
Picking a different tire for back and front is not a bad idea in my opinion, I sort of wish I had.