Horsebow archery is as old as any other archery. From as soon as man started using the bow and arrow, he also appears to have done so on horseback. Ancient caveman paintings show a the use of the bow and arrow and show it in both mounted and standing positions. The Vilafranca cave paintings, which are over 7,000 years old, show mounted and unmounted use of the bow.
If you wish to take up the horsebow and mounted archery, it is usually a great idea to be able to ride really competently first, as you will have to have complete mastery of your horse in oder to shoot from horseback; you will be steering and controlling your horse entirely by your feet, seat and balance once your bow becomes active, and then you will have to draw your arrow and aim it properly.