My horse has jumped out of his field many a time, and he's supposed to be physically incapable of jumping...

And yes, a well built horse is mechanically able to jump as high as it's poll. And an interesting fact for you...

The highest jump jumped bareback was 7'3", by a Whittaker! :D

Yes, jumping is far more natural then many other equine sports, and you'll be suprised that a lot of horses adore it!