I've had Goodyear Wrangler ATs on 2 trucks in the past, good road tired, not so well off road, and they completely sucked in the snow. I generally drive 2 wheel drive in the show with no weight in the back but with the Goodyear ATs I'd break traction way too easy; I HAD to have weight in the back.
When one truck got trashed I bought another and it came with the Wranglers, same issue, so I went for the BF Goodrich All Terrain tires. Great tires in the snow and they do great on ice too, and plenty of traction off road (not great in mud though).
BUT.....I've had 2 of those BF Goodriches get out of round on me and screw things up. I'm not hard on my truck, I haul firewood and harldy ever take it off road (unless I'm getting wood or driving in a field to go shooting), so under normal driving the belts inside seperated and got out of round, both of the tires got ate, and one wore my lower ball joint so bad it had to be replaced. Both tires had less than 10,000 miles on them and BF Goodrich didn't warranty either of them; so with spending the money on good tires and the company not helping at all with their belts seperating, I'm never buying them again.
I know a guy with the newer Goodyear ATs and he says that they've been a great tire to him