Take it from a guy who just remodeled a mobile home. The floor will not be OSB. It will probably be pressed particle board. It may or may not take paint well, and will most definitely need to be primed first. If you're planning on overlaying with plywood, I would seriously recommend against it. For the cost of even 1/4" plywood overlay and then the paint, you could re-carpet the place. Also, overlaying with plywood changes the elevation of everything. You either have to take everything out of the room (cabinets, toilets, etc) or cut in around it. Also keep in mind your door clearances. Will they need to be trimmed?
I'm not trying to talk you out of it, but just making sure you are aware of the pitfalls and the enormous amount of work involved.