Mud and dirt should show up on the car when it's driven in dirt (As an option, with an app to instantly clean the car.) If it rains, car gets cleaned. Here's some pics. You can see the VW is kicking up dirt and is dirty from driving in the dirt.
From 1.6.1 meaning a very long time till it happens as this is not on the top of the devs priorities right now. Assuming that the hopper is the next car. Hooper Hooper
I mean, they have many other things to work on instead of simply dirt simulation. Look at the latest update's changelog. Imagine having to add dirt simulation. That could maybe waste valuable time to fix other bugs to make gameplay smoother and be actually useful instead of simply just... dirt.