Here's another one for you with more experiencing driving the Ram than I, as I just got mine less than a week ago!!
I had an 07 Jeep Liberty before this. You could push the button and turn off "traction control" to allow the tires to spin with your right foot. It did however keep a component of it activated that acted as a locking diff.
It would apply the ABS to the tire spinning to overcome the torque to the tire with the most traction and power it. I had tires 2 feet in the air and it would apply ABS braking to it and power the other tire on the axel. It worked mainly at slow speed, but it did still work; and work well! It was impressive to have a front and a back tire off the ground and still move ahead without lockers.
My question, does the Ram have this feature? No place to test it with 3 feet of snow everywhere ahaha. Stuck issue for sure.