The Horseback Archers have to compete without a saddle until the second student grade. That makes learning to ride without a saddle an important part of the trainings.
There is a saying, in Hungary, that only poor people and farmers ride without a saddle.
By now, this view has changed quite a lot.
Because riding without a saddle is a lot more complex than riding with one, especially if you have learned only the latter so far.
It is one of the reasons why I am so fascinated by the Horseback Archery - the ability of the archer to become one with their mount and steer them completely without using their hands. They don't even need a bridle. Your own body is enough to make a horse do what you want. You only have to know how. (And it helps if the horse is a little trained, too.)
A saddle is a great help with holding your balance while riding. Thanks to the stirrups falling down is a lot harder. And with the bridle you can get a horse to do what you want with pure strenght, if you don't see another way.
But without a saddle you are a lot closer to the horse and to the movement. You can feel, with closed eyes, which leg the horse just puts forward, and you have to look for yourself how to hold your balance on its back. It's really interesting how different riding with and without a saddle is and I hope, I will learn a lot more about it while staying here in Hungary.