My stock-size Cooper Discoverer AT3s have been great traction-wise, including some northern MI winter driving, and muddy off-roading. I'll probably stick with AT3s even if I put on bigger tires, lift, etc.
The Cooper Discoverer works rather well in Denver mountains as well. I used the studs on them... Much quieter than a Hankook iPike and traction was just as good on Peak to Peak, etc. Nice wet traction... Not quite a Michelin MS/2 for all around use, but very good.
If you can swing the price, I would honestly recommend picking up a set of winter wheels and running a 3 season tire and a dedicated studded winter if you do much driving in the mountains. That way you can go for a bit more trail tread in the summer, and keep between the ditches by using a true low temperature severe winter weather tire.
Problem with anything that is not severe winter is that the rubber hardens up at lower temperatures and you lose traction.
If you are near a Jim Paris outlet, take a look at the Nokian Hakka 7 SUV factory Studded. Absolutely awesome heading thru the mountains at low temperatures--though a tad noisy. I'd be doubtful anyone would be so inept as to manage to skid below 35-40 mph on glare ice with those on a Jeep... Ran them on my '14 thru several polar vortices...
id look into the firestone destination AT as well, depending how rough the terrain can get- the destination LE2 is also a great tire from what ive read
Cooper AT3 are indeed a good choice. I've had them for 30k now, previously had Destnation AT's and the Coopers are far better for off road and snow traction, and smoother riding as well. Dest. AT's have a bit better steering feedback, and handling but the tradeoff is a rougher, bouncier ride, and not as good traction.