Today the general public unfortunately associates falconry on horseback to a spectacle performed in operetta costumes and to carrying raptors on the hand. Nothing is further from reality: these masquerades that have nothing to do with hunting.
Traditionally the horse is primarily a means of transport for the falconer and his bird; in visual flights, in tracking flights over large distances, its role is crucial to maintaining visual contact with the falcon (a galloping horse travels at a speed of about one-third that of the falcon, which is a considerable advantage over a person walking) so as not to lose the bird, but also to arrive quickly to recover it for further flight and to care for it.
Current falconry conditions afford the horse its true dimension in the visual flight of ravens.
A quick gait and extreme mobility must be the primary qualities of a horse for falconry. Choice of horse, certain issues in its preparation.
Galloping quickly, making a short stop, turning, recommencing a gallop without flinching over difficult terrain and small natural obstacles: everyone says that their favourite breed fits the ideal bill. The Iberian horse, the polo pony and the cutting horse could appeal to many; the preferred horse of a master of hounds is an Anglo-Arab whereas his wife swears by the thoroughbred Arabian horse; my preferences lies with the thoroughbred. Widely used by hunters, the trotter lacks, in my opinion, the high speed required and is more difficult to balance and to render highly mobile.

Image :
Henri Desmonts and his horse Jim training