The equestrian
A person who races a horse is a jockey.
A person who rides horses (mainly thoroughbreds) is called a Jockey
There are several synonyms for "a person who rides a horse"bronc bustercowboycavalrymanhorseguarddragoonequestrianjockey
The person who rides a horse would be called either a equestrian or horse rider, but if the person only rides in shows, they may also be called show riders.
a person who rides elephants is called a mahout
The proper term for the skill would be 'horsemanship'. When refering to a person that rides you would call him an equestrian or equestrian sports.
a bicyclist
A ballonist.
A jockey is the term for someone who rides horses in horse races. Or more specifically a horse jockey.
a person who rides a horse carriage is a horse carriager,horse groom,horser,horse carriage man,horse guard,horse carry,
A mustang is a (horse) and a person rides it.
you can call it a balloonist
A jockey - or driver.