My mare is a very red-tone chestnut (well, in the summer). Our colors are pink and purple. Our "traditional color" is navy - which looks gorgeous on her.
Of course, you have a *him* not a *her* so pink and purple wouldn't quite fit. LOL. Turquoise looks stunning on chestnuts - or if you wanted something less "bright", teal is a little more toned down than turquoise I think.