Yeah, the idea is to cut through.

If there's snow, then it seems like a toss-up to me. However, it seems like the knobby tire should go on the front if you're going to mix and match. You want more traction on the front tire, 'cause losing traction there sucks.

If there's ice, I'm pretty sure anything short of studs won't help at all - you'll just be sliding around no matter what.

Big tires could help protect your rims from chunks of ice or concealed debris in the snow, plus you'd grip better in the patches of mud that form during the winter (at least where I'm from).