I coat lost foam casting patterns with a thin mix of the sort of plaster used for jointing drywall (a small sack goes a long way). The mix is about the thickness of cream, and the pattern is simply dipped in it and allowed to ‘drip-dry’. I wasn’t trying to get a good finish – it is to prevent the casting sand collapsing into the mould at the instant the hot metal replaced the foam. Lots of people recommend latex paint, but it never covers properly, as Simon noted.
It might be possible to do this, then clean up (sand?) the plaster, and paint afterwards – for casting, I never cared about the outside finish. I assume you are using the ‘hard’ dense coloured foam used for building, which can be machined and sanded very smooth with care, not the white packaging type foam.
Another consideration might be that this stuff has horrible ‘attractive’ properties due to static electricity (I think) – I find I can get it apparently extremely smooth to the touch, but looked at closely in a strong light, it is covered in the dust produced by sanding it – maybe you can take it into another room and blow the dust off.