Yeah, the Dueler tires you've got on there (I have the same ones) are not going to be great in mud. I like the Duelers a lot for the spring/summer/fall, as I can get pretty good mpg with them. 21-22mpg at 80mph with my 5.7 w/ eTorque 4x4, 3.92 gears.
However, it only took me a trip or two in the snow up here to realize what you found out. Basically, they’re... ok, but not good in snow (and I assume mud for the same reasons). Their ‘street tire’ design that nets decent mpg is the same reason they're subpar in less than ideal conditions.
If you're looking for mudding tires, theres lots of alternatives. Bridgestone All-Terrain KO2’s were what I had on my old truck (‘12 Nissan Titan Pro-4x), and I liked those a lot. Killed my mileage (17 highway down to 14 highway), but they looked great and performed just as well. Likely would've got 50k+ miles out of them too if I hadn't traded the truck, just need to rotate them with every oil change.
Nitto Ridge Grapplers seem to be very popular on the various Ram forums I’m on, but I don't have any personal experience with them, same with the Falken Wildpeaks. Bridgestone also makes (or made?) a Mud Terrain tire, but I recall them being extremely pricey. Happy hunting!