Other forms: ridings
Use the word riding for the sport of maneuvering a horse while sitting on its back. So when your friend invites you to go riding, you'd better be prepared to climb up into a saddle.
You can also call this sport horseback riding, or if you want to get really fancy, equestrianism. Riding involves, of course, staying perched on the back of a horse while it trots, canters, or gallops along. There are a lot of additional variations on riding, including horse racing, rodeo events, and dressage, which involves dance-like movements that are judged on how athletic and graceful the horse is and how relaxed the rider appears.