I think that one of the key elements on many mud types as well as snow and grass is how when your wheels slip thread gets filled with mud and tire grip is greatly reduced. What essentially happens is that your thread becomes non existent and tire starts to behave like a slick. Wet grass and thick mud are especially bad in this. In addition to current friction changes when tires slip, some control in groundmodel how tread coefficient decreases with slip amount and for tire how well tire clears up at higher speed might provide more realistic mud driving. As a new parameter that defaults to current behavior (no change) it would not affect current mods or do huge complications, but there is always potential other challenges. Grass is essentially mud underneath it (unless grass resides in very dry areas):
That's more of a terrain function than a tire function. I believe spin tire-like physics were suggested quite some time ago. I'm guessing it's not going to happen for 2 reason. A) The game already has wayyyy too much physics simulation going on. B) They want to focus more on just car behaviour than terrain behaviour.