I have Cooper AT3 30 x 9.5R15 on my stock XJ.
About 1000 miles on them. Really good on wet pavement. Never slip, never hydroplane (even at 70 mph). Great handling-cornering wet or dry pavement. Soft comfortable ride. Very quiet.
Great on gravel roads. Never spin, even when very steep.
Great on mud. I've been mudding 3 times on wet trails that have hard slick mud in places, and soft mud 4" deep in places. I did it easy in 2wd (open diff) with minimal wheel slip. No spinning.
Haven't tried them yet on Winter conditions or sand.
AT3 is a great tire!
A very similar tire is Hankook ATM. OP might want to consider ATM.
According to 4x4 mag and truck reviews, and Consumer Reports, the Hankook ATM looks and performs very similar to Cooper AT3, but with a few differences.
AT3 rides slightly softer. AT3 is as good as it gets for AT ride comfort. However, ATM rides softer than most ATs. So both offer a comfortable ride, but AT3 has a slight comfort advantage over ATM.
AT3 is very quiet. More quiet than other ATs. The AT3 is as quiet as an all season car tire. The AT3 is silent to most people. The ATM makes a little noise, more than AT3, but is quieter than most brands of AT.
Both are rated (by Consumer Reports) as excellent on snow. So no difference on snow. The AT3 is rated "Fair" on ice. So it's OK-adequate on ice. The ATM is rated "Excellent" on ice.
I think the ATM's higher ice rating might make it better for the OP.
Several reviews by 4x4 mags and by users (including myself) say AT3 good on mud. The ATM is good on mud too, but not as much as AT3. The AT3 is better on mud.
My AT3 took a lot of weights to balance.
But they run smooth and without vibes.
So the balance weights worked.
According to reviewers, the ATM is well balanced from factory and takes minimal weights to balance.
AT3 has slightly less rolling resistance than ATM. So possibly the AT3 might give slightly more mpg.
AT3 has 55K warranty. ATM has 50K warranty.
Over all the performance (and appearance) of these two tires is very similar. BTW - They look like ATs, not car tires.
The key differences (IMO) are the AT3 is slightly better in mud (though ATM is good too), and the ATM is slightly better on ice (though AT3 is adequate). I also like the AT3 best ride (soft ride) quality because I have a bad back. The ride quality is why I bought AT3, but the ATM rides almost as soft.
The key point for the OP is the ATM is slightly better on ice.
I don't get much ice. So AT3 will be good enough for my occasional ice needs, and I've been enjoying it's slightly greater mud ability.