1) Athletics 2) Horseback riding 3) Horsemanship 4) Riding 5) Sport 1) Horsemanship 
horseback riding
• (n.) A riding, or the act of riding, on horseback; horsemanship.
Eq`ui·ta'tion noun [ Latin equitatio , from equitare : confer French équitation .] A riding, or the act of riding, on horseback; horsemanship. « The pretender to equitation mounted.» W. Irving. 
The art of riding
noun the sport of siting on the back of a horse while controlling its movements
the art of riding. Equitation classes are judged on the rider
The art of horse riding.
The position of the rider on the horse
the act or art of riding on horseback.