Muddy roads

I myself wouldn't use Celluclay on styrofoam... It doesn't dry well on it and has a tendency to curl up because it shrinks as it dries.. Adding white glue to the mix will help preven that though...

Using styrofoam as a base, I'd carve the road, ditches, and the ruts into base itself,  cover it in sheetrock mud (mixing a generous dollop of white glue into the stuff will help it stick on the foam), and make the tracks, footprints, etc, in the mud with the vehicle itself, since the stuff is, esentially, mud...  You can color it ahead of time with tempera paint, or paint it after it cures...

You'll still want to glue the foam to a more rigid base material though, to keep it from flexing when you move it.

You are likely to receive a dozen replies with different ways to do this and all of them work, I suppose.

What I would do is carve out any deeper tracks in the styro. Coat the base in about 1/4" of Celluclay mixed with darker earth toned, cheap craft store acrylic paint. Be sure to keep your mixture from being too wet. I'd replace most of the recommended H2O for this mixture with white glue. You can also add some fine sand and / or railroad modeling ballast if you want to bring some earthy texture to the mix. I'd personally use the mix without the ballast, and then I'd sprinkle it over the wet base where I want it, and then work that into the Celluclay. This way, I get more control over how my terrain will look.

After it's applied, you can lay down tracks and footprints to suggest the "traffic" using spare model parts. Let the base dry 24 - 48 hours, and then use light and dark earth tone washes and dry brushing to shade and highlight the road. After this, you can seal it to protect the paint, but might not be necessary.

Let that all dry. You can simply shoot some glossy sealant over the whole base, or you can hand-apply a glossy acrylic medium over the wet surface mud and deeper puddles in the road. Again, I get more control over the look of the terrain this way. I use Liquitex Artist Acrylic Gel Medium, glossy. Can be found in nearly all craft and artist's supply stores. Dries glossy. I'd build up layers to do this, rather than slopping it all on there. .

Again, you will get various methods provided in replies. Experimentation is key, so use the best method for you.