I have painted on trailers (artwork). You'd first have to determine what the exterior is made of (steel, aluminum, fibreglass?), whether it's been painted before and with what. I would certainly seek out trailer restoration websites/businesses for advice. My limited experience says: clean it very well first. If it is very shiny (unlikely, if it's older), give it a light sanding or steel wool-ing, and dust any residue off. I've had good luck with latex exterior paints on fibreglass, oil based enamels on metal, and there are high adhesion latex paints available. Paint will likely fail if there is any flexing of the surface, likely not a consideration if it stays parked. Have fun!