Can you provide a published source for this horse-shooting requirement idea?
Think about it. It is hard to train men to pick-off mounted horse soldiers without plugging a pony.
On the other hand, shoot the horse, The horse stumbles, falls and so does the rider; injured rider is less of a threat. Dead and injured horses create obstacles for their dismounted riders and stumbling blocks for other horses. Sound battle plans.
So sad for the horsey people.