General terms:
* Rider: This is the most common and general term. It simply means someone who is riding a horse.
* Horseback rider: This is another common and general term, emphasizing the mode of transportation.
Specific terms:
* Jockey: This term is used for someone who rides horses in races, especially professional jockeys.
* Cowboy/Cowgirl: This term refers to someone who works with cattle and rides horses as part of their job or lifestyle.
* Equestrian: This term is used for someone who participates in equestrian sports or enjoys riding horses as a hobby.
* Mounted: This term describes someone who is riding a horse, often used in a military or historical context.
* Horseman/Horsewoman: These terms are less common today but were used to describe someone skilled at riding and handling horses.
Other:
* Amateur rider: Someone who rides horses for pleasure or personal enjoyment.
* Professional rider: Someone who rides horses for a living, such as a trainer, instructor, or competitor.
The best term to use depends on the specific situation and the type of riding being done.