I currently ride horses, and I hope to all my life. From my hands on experience, I can say that riding has made my legs stronger, as well as my upper body. The horse may be getting good exercise, but the rider is getting a pretty good work out as well. Especially if you ride without stirrups!
Horseback riding is an excellent source of exercise and if you can do it, you should. It strengthens the body, and it's cool to be riding a horse and forming a bond with it. It's time people realize that and get more physical exercise. It's all good for you, you know?
Horseback riding is hard. Without a doubt it makes you stronger. I ride horses, and all horses have stubborn sides. When a horse has a stubborn side, it is guaranteed that there will eventually be a battle between horse in rider. To me, a battle with a horse is tug of war, accept with a 1500 pound muscle machine. If that doesn't convince you, sit in your chair like you would sit on a horse. Bring your feet off the ground and grip the sides of the chair with your knees. Now, without letting your feet touch the ground, try raising your butt up and down at a even pace. Equestrians have to do this every day. Also, the chances are that if you ride horses, you do barn chores. If lifting a 50 lb. Bag of food doesn't strengthen muscles, I don't know what will.