I wheel primarily in the Southwest deserts and also use my rig for a DD. The original 31" MT/R's gave me over 48,000 miles of excellent service both on and off road although the shoulder lugs do chunk a bit in sharp rock. I replaced them during a suspension lift but would think I could have easily gotten 55k miles out of them.
I replaced the OEM's with a set of 35's that have given me the same stellar results I enjoyed with the originals. I don't see much mud and then, certainly not the sticky, gumbo stuff found elsewhere, so can only say that I've "heard" they pack up and don't clean out very well, pretty much rendering them useless. Can't comment one way or the other on ice or snow.
I ruined the two front tires while on a trip in Oklahoma a couple of months ago. That was a long story that's way to embarrassing to go into here but they were replaced with 2 new MT/R's w/Kevlar (all I could afford at the time). That was at around 65,000 miles. With only 17,000 miles on the ones I trashed, they looked practically new with lots of tread left. Shucks!
Anyway, I am in the process now of obtaining and installing 3 more 35x12.50R15 MT/Rs with Kevlar on my Champion beadlocks. I'm swapping out the spare too, since the inside sidewall shows some heat damage from being exposed to a fire I had back in November.
I expect the asymmetrical tread pattern to perform better than the "old" design in the type of terrain I run. If mud was a major factor I'd probably be running something in the Interco "Swamper" line. I'd have to do a little more research here but this seems to be a popular choice with some of the Southern boys and girls.