The concept of armoring one's horse was called barding and in Alexander's past life history, the practice was thought to have been first extensively developed in antiquity in the eastern kingdoms of Parthia, which was in modern-day Turkey, Syria, and Iraq.
Meanwhile, in this time period, this had yet to be introduced as though they would dress their horse in colorful clothes, as Amenheraft did with his horse in a start golden color, but the concept of fully armoring one's horse with leather or fabric had yet to be introduced.
Thus a typical Adhanian cavalry unit would consist of only light cavalry, being recruited exclusively from noble families or those related to him somehow, either by kinship, peerage or by land.
This was both because it was a political statement to let only the blue blood ride horses into battle, but also because it was very expensive to own and maintain a horse.