a cheetah jockey and a person that rides a cheetah carriage is called a cheetah rick, cheetah rickshaw,cheetah rickshaweror a cheetah rickshaw driver or a broccoli
Chair
a person who rides elephants is called a mahout
a bear jockey and who rides a bear carriage is a bear rickshaw driver,bear rick,bear rickshawer,bear rickshaw manand workery
a person who rides a horse carriage is a horse carriager,horse groom,horser,horse carriage man,horse guard,horse carry,
a person who rides donkeys is called a donkey jockey
A person who rides horses (mainly thoroughbreds) is called a Jockey
Once may find horse drawn carriage rides at many convenient locations. Horse drawn carriage rides can be found at major cities worldwide, as well as tourist attractions. Many suburban and rural areas offer this attraction too.
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 cyclist.
Commuter.
A uni-cyclist.
In India, a person who works with, tends to, and/or rides an elephant is called a mahout.
That is a jockey