So I’ve done this (and mounted riflery ) and step one is to make sure the people can shoot from the ground without endangering themselves and others. Seriously, if they can’t put the arrow in the target 9 out of 10 times at 15 yards, do not let them try while on a horse.
I’m going to assume you’ve already got a horse that is controllable from the seat and legs. If they need to touch the mouth to rate the horse, the horse is not far enough along in it’s training for this. I used my 3rd level dressage horse. Most of the other horses were either dressage trained, reiners or working cutting horses.
For the horses themselves, it’s a lot of desensitization. Bows make a noise, some worse than others. Arrows make a noise when they hit. Get the horse used to it on the ground first. I suggest you have the horses just hanging out behind the archers while they shoot. You want to stay at this stage until the horse is barely reacting when the arrow is released. This is very variable … my arab barely acknowledged something was happening but two of the quarter horses lost their minds the first few times they heard the bow.
Get the horse used to the rider twisting and moving all over the place in the saddle, first at the stand still, then walk, trot, canter, all without the rider touching the reins. They should be able to go up & down the gates with their seat & legs. A lot of horses want to speed up in a list … something about having a nice clear path defined. You need to be able to half halt them back to a steady canter without grabbing for the reins.
You should practice “accidentally” knocking the horse with the bow and equipment , again starting at a stand still. The horse should be listening to the legs, not shying sideways if the rider twists suddenly or if the horse gets hit on the shoulder with the bow. The list is often made up of ropes between stakes (think how they mark a course for eventers). It’s not pretty when a horse spooks sideways, goes through the ropes and is now tangled up in the list and being chased by the poles.
Next is mounted, stationary target practice. This is learning how to shoot from both sides of the horse and maneuvering your equipment. This is a lot more awkward than you’ll ever think it is until you try it. From there, you work your way up. Walking while shooting from both sides, trotting, etc. If the horse starts to wig out, step back and make sure it’s comfortable with the previous level.
I highly suggest the archers learn a right side pull. It’s a pita to have to get the arrow up & around the bow while cantering for a standard left side pull. If they’re looking at competition mounted archery down the line, they need to learn a thumb release or such. A mechanical release like what compound bow hunters use is a no go. There are no arrow rests on mounted archery bows, so that’s something they need to relearn if they’re traditional archers. Saluki bows are the gold standard for mounted work and they have a lot of information on their web site and a lot of pretty pretty bows to give you an idea about what’s appropriate.
It looks like the Mounted Archery main web site has some tips on getting your horses ready - http://mountedarchery.net/about-2-2/…ng-your-horse/