I'll focus on the directly archery related things. I think it's quite obvious that the horse is heavily moving and thus you've to learn to absorb this movement in your hips.
The main difference is, that you need to be fast. You don't have time to sit in your anchor and focus. You've to look, draw, anchor, release in just a second.
Horsebows are also commonly shot over the outer side (the opposing side of your bow-arm) of the bow. The arrow lays on your thumb.
The release technique for a horsebow is also different. They use the thumb technique.
In addition to the popular, so-called “Mediterranean” technique for
drawing the string using the index, middle and ring finger, there is
also a method for drawing the bow that involves the thumb, which is
still used in Asia today.
This was the technique employed by many
traditional riding people such as the Mongols, Tartars and Huns. Even
in Turkey and Hungary the thumb technique is still widespread today.
With the thumb technique the arrow is usually placed on the right side
of the bow (whereas for the Mediterranean technique it is on the
left), so the arrow doesn’t fall off the arrow rest while the archer
or his horse is moving. [If you are a left-handed archer, it's the other way around of course.]
Another reason is that when using a short bow
with a large draw the angle of the string when fully drawn can be very
acute. Finding room for two or even three fingers can be difficult,
causing a lot of pressure on the fingers or even on the delicate arrow
shaft.
The thumb technique makes it easier to reload the bow and there
is a smaller risk of injury as the arrow does not need to be inserted
between the string and the bow arm. This means the tip of the arrow
won’t poke you in the hand or in the bow, as often happens with the
Mediterranean technique.
With the same amount of effort the thumb
technique gives you 1-2 inches more draw compared to the Mediterranean
technique.
The spine value of the arrow does not have to be perfectly
matched to the bow with the thumb technique. This was a big advantage
for antique archers in battle, as they could simply pick arrows off
the ground and shoot them again.
Of course you don’t need a horse to
use the thumb draw. These days the technique has many supporters who
enjoy this form of shooting – or rather releasing. However you still
get quizzical stares when you arrive at archery practice with a ring
on your thumb.
From Bogen-Daumenring
Mention three things in this picture:
- The far-behind-anchor (nearly behind the neck)
- The thumb-technique
- The arrow lays on the outer side