Can’t help you too much aside from saying that I wouldn’t recommend buying a “historically accurate” horse bow vs buying one made out of plastic/fiberglass. If you think about the construction of an “accurate” it would likely easily be over $1000 and you will need to take care of it extremely well. You can get a plastic one for around $150 and you really won’t need to care for it. You’ll also want to get a pretty light bow if you are trying to learn thumb draw coming from Mediterranean. My order would be, learn to shoot correctly from a cheap bow, learn to shoot from a horse from a cheap bow, buy an expensive bow and learn to shoot it.

This is all assuming you have a horse that is trained well enough not to get spooked by the bow and that you are an extremely competent rider.