“Natural horsemanship” is an oxymoron. There is NOTHING natural in the horse allowing a member of The World’s Most Successful Predator Species to climb on its back!!! 
When we take the horse out of its world and bring it into the world of humans we are wise to use our intelligence to figure out how we can make use of the natural instincts of the horse to accomplish a task and to suppress the horse’s natural instinct to flee after dumping the human into the dirt.
I’m of mixed mind about Buck. Don’t know anything about Warwick, Andrew, Stacy or Harry.
You can download Vladimir Littauer’s book Common Sense Horsemanship for free in a number of places. It’s very good but oriented to practice, not philosophy. It contains a seven month program, in detail, for using both ground and saddle work to make a fox hunting horse. A good hunt horse is about as nice a mount as the average horse owner might like to have. Capt. Littauer (late of the Imperial Russian Cavalry) tells you how to do that.
If you’ve never read them, you should also read the two oldest, complete, extant pieces on horse training. They are very short, to the point, and most of the modern stuff is functionally commentary on them:
On Horsemanship by Xenophon. And The Cavalry General by Xenophon. Both were written about 400 B.C. but are completely relevant today. You can find them on Project Gutenberg:
https://www.gutenberg.org/files/1176/1176-h/1176-h.htm
https://www.gutenberg.org/files/1172/1172-h/1172-h.htm
Utube is full of videos but, like much of the Internet, is 90% dross. You’ll have to kiss a fair number of frogs to find your “training prince.” 
Good luck going forward.
G.