I too have built and flown model aircraft made out of brown paper-covered white polystyrene foam. One of the more popular 2m glider trainer designs at the club I used to fly with made use of this construction method for wings, fuselage and tailfeathers, the only wood being the pushrods, spars, towhook mount and servo mounts. Some people got creative with the colour schemes, using thick coloured wrapping paper instead of brown paper. The things flew well, were surprisingly tough, and very easy for beginners to repair. They also had the advantage of being affordable enough to be almost disposable, making the inevitable beginners' crashes a whole lot less heartbreaking.
Another method I am strongly considering using is one I tried a few years ago when making a model buggy bodyshell. I carved the plug out of white foam, covered it in brown packaging tape, blew a hairdrier over it to shrink out the wrinkles in the tape, then covered it with glass mat and polyester resin. The tape protected the foam, and made removal of the plug a lot easier as the resin didn't adhere to it. I then brought the outer surface to a good finish through the application of polyester resin and microballoons, along with plenty of sanding!