Trivia, blindfold them and get them to feel differed horse feeds and guess which ones a which, maybe completely undo spare bridles and get them to put them back together
On a horse: egg and spoon races, cowboys and Indians
Musical chairs on horse. Questions relay games. Obtsacle courses
Bareback tag at walk/trot - if you're allowed to have the kids ride in halters
Jousting with pool noodles!