My first car had a styrofoam body made out of 1/2" blue insulation from Lowe's. I formed it over a schedule 20 PVC frame and glued it together with white gorilla glue. In order to make it more durable and to take paint, I coated it with Styrospray 1000 which is a difficult to obtain industrial coating.
The body was very light and fairly easy to put together, but really wasn't durable at all. The coating would crack and flake off pretty readily. Maybe I should have used more of it... I dunno.
Anyway, I recently stumbled across a different product that I used to coat my styrofoam mirror backs. It's Weldbond glue.
It coats nicely with a foam brush and I expect it would roll on nicely with a roller. It hardens to a tough yet mildly flexible finish and takes paint well.
When I first debuted my original car there was some interest in how I constructed the body. I definitely wouldn't do styrofoam with the Styrospray again, but I might consider it with the Weldbond.
Try Smooth-On Epsilon Pro for coating and hardening foam. It's a thixotropic coating that's paintable, sandable and impact resistant. I use it to make foam bucks for fiberglass casting.