Kevin, I normally dry-brush tyres if I want a dirty, dusty or muddy look.
The colour depends on the terrain in question, and the season/weather of course. But, I normally start with a colour a shade lighter than what I THINK it should be, and build-up gently, not forgetting to feather outwards on the tyre (towards the axle) around the top edges of the tyre. If you want to make it look like a slightly heavier coating, say, mud, then give the tyre(s) another, light, dry-dusting, this time with a little more paint, stippling vertically onto the tyre tread and or wall. With enamels in particular, this will leave a slightly heavier, 'grainy' deposit, which looks more like lightly 'clogged' mud. For a dry, dusty type of earth packing, such as sand or sandy soil, leave it matt, as it comes. If you want it to look like fresh, wet mud, then give it an uneven coat of gloss varnish - Johnson's 'Klear' (Future) is ideal for the latter.
But, as Chris has just pointed out, have a go on something of a similar shape colour first, just to check that the colour/consistency etc is acceptable.