Why use a horse for falconry?
As someone who uses horses for falconry displays and teaching, there is an assumption that all I do is for show, but that is not the case. The whole team of seven ex-racehorses I keep do falconry in the field as well.
A horse can take pursuit falconry and eagle falconry to a different level. Given the right ground, you can position yourself quickly and quietly to get the best slips and flights. You can follow a flight well, rather than being left as a spectator looking at your gps tracking system to work out what's actually happening! And of course it's fun working horse and hawk (and human) into a team that works so well together.
Working hawks and horses is taking two extremes, the ultimate flight animal working with the ultimate predator. So firstly you have to encourage both animals to like each other (not just tolerate each other) as it has to be a working relationship of trust.
To this end, the horses are rarely exercised without at least a hooded falcon on board, and the hawks are rarely exercised without a horse being present or part of the exercising. Both sides have to be completely relaxed and accepting of the others presence.
Once they work together in the field, the relationship becomes so much stronger, as it does with humans and hawks. We’ve yet to find a horse that doesn’t love field falconry (though several have more sense than to put up with the teaching side).
The horses learn quickly to follow the flight itself, and spot quarry - but they also learn when to stand still and when to go. Good pursuit falconry is fast and reactive, so the horse needs to go from gallop to stop, and then wait patiently while I’m sorting out a hawk on a kill, or to be tethered somewhere safe and wait while I hike on foot into an un-rideable bog!
Sometimes they may need to be abandoned on the spot and wait patiently for me to return (and carry on standing) while a wayward hawk decides coming back to the horse is easier than coming back to me.
Horses and hawks, when given a chance, is a match made in heaven.