I have my grandfather's 'Wonder Book of Soldiers,' c1914, which has a couple of photos of British cavalry practising rifle (SMLE) and pistol shooting from behind horse "trained" to lie down. Possibly one of the factors is that, if caught in the open, the prone horse is less likely to be hit, and if you can train it to lie down, you might as well take cover behind the poor thing anyway.
Any expert know whether deaf horses are less or more liable to get spooked?

Hi Mike B!

The real trick to teaching horses to lie down was by twisting their heads away and around from your body and round back towards it's rear-end and towards yourself and pulling the animal down. This was very physical. Once down they are pretty docile.

Rent the video "Geronimo" and see the perfect real life example. And you are right, standing targets get hit; laying are smaller to hit. Regarding horses who where deaf, I don't know, but it is a fascinating point. Anyway, thanks for your interest and ...

Happy Collecting!