Pinholing in color is easy with 35 mm or 120 film, and not too bad with 4x5 (which costs more to process, but is otherwise better). Just expose the film and (especially with 35 mm) hand it over to a commercial lab for processing -- Costco charges me $5.22 to develop and scan a 24 exposure roll from my 35 mm pinhole camera, and I can get 120 negatives developed locally as well (even 4x5, if I can ever find the lab people keep telling me about, though 4x5 color gets expensive in a hurry). Doing so with color paper would require being able to process RA-4 in order to develop the negative and contact print, and CC filter the light used for contact printing to correct color (which will otherwise tend to be too yellow because of lack of the orange negative mask).
It would probably be a good bit simpler, and possibly cheaper (given no need to make contact prints) to work on Ilfochrome; you can find a filter that gives good results in daylight and stick with it or add correction filters to it as you would with slide film, and the print will develop directly to a positive (though it's also possible and not even very difficult to reverse RA-4 papers); contrast is controllable by choice of first developer formula (the Beers developer family is said to work well).