Another possibility from my experience owning a forward TB–ones like this one that know their job sometimes see a green rider hanging in its mouth as a sign that green rider doesn’t have a clue where she is. The horse then responds with an, ok, I got this, and takes over to the jump, which may mean anything from being a little quick to “freight train”. I am a quiet rider but when I bought my horse like this (an experienced horse but not yet at the stepping down phase), I didn’t make the horse get hot, but I was very frustrated when I would pull on the reins to ask for a quieter distance and the horse would respond by wanting to run. It wasn’t until I talked to the trainer that previously had the horse that I learned that she’d just take over because being handsy is what the previous owner would do when she felt lost and didn’t see the distance.
Ultimately, what everyone is saying about aids is correct, particularly the comments about the half halt, but also this rider may need to earn the trust of the horse. Even after my horse developed confidence in me to find the distances and stopped the running nonsense when I meant “whoa”, I noticed she’d still get quick in the same way with less experienced riders when I went to sell her to someone who’d give her an easier job. In some cases, the prospective buyer wouldn’t use enough hand, in some cases too much. In all cases, there was no understanding of the correct half halt that has been described, and the horse knew immediately. Auto pilot for these horses just happens to be a lot faster than the kick ride packers.
The alternative to the above is the jerk
– Even my kick ride hunter (who became made up but was no packer) did the same thing when I sold him to a more novice rider. I’d taught him with his gigantic stride to wait in the lines as a green horse when he wanted to leave strides out, especially towards home, and I went on to show him for a couple more years without that behavior, but he reverted to that habit with his new owner I guess just because he could.
The good news is that the rider can be trained to deal with both situations and the horse will develop confidence and respect. However, if you try for a long time and it’s not happening, then it’s probably a fatal personality conflict between the horse and rider and it might be a better learning experience for the rider to get a horse that compliments her better.