Equipment for mounted archery is evolving as the sport develops. Currently, there are few hard rules and much discussion… join in!
As you might surmise, shooting a bow from a moving horse is different from standing on solid ground. Mounted archers develop their accuracy by feel and repetition, using intuition more than aim. Archers pull and nock their arrows very quickly and without looking at their hands (the top archers currently shoot 9-12 arrows accurately in 16 seconds, yes, from a galloping horse).
The equipment and shooting styles reflect this.