lol, i've always wanted to see a black ninja horse at a costume contest.... for tiger stripes your best bet would be paint, unless it happens to be warm and your horse will sweat.... then you'll have runny tiger splotches! If it's going to be cooler, try a cooler (lol) and paint stripes on it. You could also get a black cooler and cut out shapes and let your horse's red color be the base, and the black cooler the stripes. do you need a saddle?
Also, you need to be the "tamer" so maybe use part of a martingale or something as a "collar" You can add silver tinsel or pipe cleaners to it to make it look real. You could also attach teeth or stripes to the halter/bridle. Make sure you get your horse used to whatever costume you decide on... i've seen SO many poor horses forced into weird costumes and then spooking! I swear, costume class is the class most people fall off in, lol.