I am running Firestone destination AT's right now, they were rated highly for snow and rain, and I am happy with them. Ran Goodyear Wranglers before that, and I would have bought them again, but their price went up ridiculously high, and the firestones were rated higher. I am not sure if they are still available, but the Dunlop Mud Rover was a good tire for me. Don't let the Mud in the name throw you, they are more like a very aggressive all-terrain, similar to Goodyear AT's but spaced out a bit more with larger lugs.
I have 5 sets of the BFG AT's on various vehicles, and were my go-to tire, but when they changed manufacturing plants the quality went to crap. That was a few years ago, they may have gotten back on track.
I will buy Michelins for my bikes, not my cars. They are an 'old-mans' tire, (no offense, I am one now) and the endorsement is "they last forever". They do, because they are made out of rock and provide no traction. Couldn't wait to get them off my Suburban. Put on BFG's, ABS didn't go off half as much, and must have cut 50ft off 60mph braking distances. YMMV