I have a 2010 Dodge Ram 3500 Cummins w/auto. I bought it new and ever since I have owned it when I get in snow pulling a trailer in 4wd up in the mountains at slow speed when ever it breaks loose I get severe hop in the rear. This has caused me to get stuck more than once because of the need to let up and stop the hop. Has anyone else had this problem and what did you do to fix the issue?

Have a limited slip rear end in it?

Yes it does

Hhhhmmmm..... How old are the shocks? Is the truck lifted at all?

Everything is original equipment 47K miles on truck. Only use it for towing is why miles so low. Did it with the original Michelins and now I have Cooper ATX on it and it still does it

Coils or leafs in back? Think I would start with new shocks.......

Leaf springs no sway bar in rear not that that matters

Is dodge still using blocks between the axle and springs to get the right ride height? If they are, might consider a shackle flip, and eliminate the blocks. They give the axle a nice lever to twist the springs around with.....

I'll bet your rear shocks are worn. They wear out slow so you don't notice it, but when you replace them, you notice the difference big time.