Good question. Most doctors advise their patients to avoid activities that would put them at risk for another fall with an outstretched hand. Patients are usually encouraged to be as active as possible. Activities that involve sudden twisting should also be avoided.
Horse back riding is considered a high-risk activity for orthopedic injuries. Although your wrist might be protected in the cast, a fall on that hand could reinjure the wrist.
With the wrist in a cast, the elbow and shoulder joints are at increased risk of injury. The impact transfers the force to these areas.
You may want to ask your surgeon this question. He or she has a good idea of the stability of your wrist and may have a different opinion. It's your doctor's opinion that counts the most.