I don't show (yet!) but I bathe my mare three or four times a year. And her tail and mane get washed probably six times or so. (She has an over two foot long mane and her tail drags the ground now, so when they when they get too filthy I wash them but not the rest of her.) I also hose her down with no soap when it's really hot, and she LOVES it.
**I must not forget to thank the difficult horses, who made my life miserable, but who were better teachers than the well-behaved school horses who raised no problems.**