Well, according to the elemental subtype, they can gain simple weapon proficiency if they take a humanoid shape. And while they do not gain armor proficiency, the possibility is not forbidden.
That, combined with the fact that they lack things like amorphous and such, seems to indicate that elementals have a physical form. And since it directly references a humanoid shape, then nothing particularly stops them from riding things it seems.
So the question here is whether they can stay on a mount when they become one with the earth (This is more of an earthglide quesiton really). Well, they do have a burrow speed of their own, and nothing says that the earth elemental HAS to use earthglide while burrowing. If they wanted to stay on, then it is the same as if any other creature wanted to ride a burrowing creature (not to familiar with that bit myself).
So yeah, make them into something more interesting than 'Imma Rock Man, Imma smash you'.