General terms:
* Young rider: This is a broad term that can be used for anyone under a certain age limit, which varies depending on the equestrian discipline.
* Junior rider: This term is often used in competitive equestrian sports.
* Pony rider: This is used when the rider is specifically riding a pony, often associated with younger children.
Other options:
* Jockey: This is used specifically for riders in horse racing.
* Equestrian: This is a more general term for someone who rides horses, but doesn't necessarily imply age.
* Beginner: This can be used to describe a rider who is new to horseback riding, regardless of age.
The best term to use will depend on the specific situation and the age of the rider.