I found a light-weight modeling clay called Modelite made by Cra-z-Art. It is a finer and easier to use Playdoh-like material which air dries. It dries softer than Playdoh and has a little give to it when dry. I rolled out a ball of it in a zip lock bag to a uniform thickness and applied it over the base. I first built-up the base with cardboard pieces to reduce the amount of Modelite clay I would need. I also cut holes in the base so the model's wheels would be lower.
The base is far from finished but you can see how this might work for your next model project. Mine is a 1/35 Trumpeter SFOR USMC LAV-25 stuck axle deep in mud.
Crayola makes a version of this and probably others. Whichever brand you buy make sure it feels soft when you squeeze the bag.
It does dry-out if left open, so store it in a zip lock bag. I got mine at the local craft store next to the Playdoh. -Bob Walls