Hmm. What I see in both of those videos is not so much of a bond, as horses that are well trained. I guess to me a bond if more of an emotional connection to each other.
For instance, in the video above of the Icelandic, I would imagine that is a result of a good "join-up," correct? I have done the same things (only without obstacles) with my long yearling. In an inclosed area he will follow me around just like that. I can change directions, etc., and he will follow me at liberty. And yet I don't feel like we have a good relationship. He is pushy and always testing his limits. I don't know if I consider him to be bonded with me. But if this is what bonding is, then maybe there is hope for us and my expectations are too high. Because in the pen, he is almost just like the Icelandic. But he doesn't respect me outside the pen and I am often on the verge of giving up and calling us hopeless.
The first video is pretty amazing! But again, I see those as horses that have been well trained (and I would bet they were trained in the traditional way with tack) and now they are perfected to the point of performing without tack. And it is very amazing! I can't do this with my horses. But I don't know how much of that is "bond" and how much is just consistent training.
I guess it begs the question "What is a bond with a horse?" To me, it would be an emotional attachment that the horse really prefers to be with me and shows me friendship when in most normal circumstances the horse would choose to do something else. Ie, if a horse came to spend quiet time with you instead of grazing in a pasture. Or a horse would show you affection/friendship when they don't do that with anyone else. That is what I call a bond.
What do you guys consider a bond to be?