This happens on both standard handling horses like the Tennessee Walker, and superior handling horses like the Arabian:
When running through woods, the horse drifts itself to certain sides of trees in spite of where I move the joystick.
I want to run between two trees, and it wants to run around them. I push the stick left because my horse is automatically trying to move right. Guess what happens. Yes, I plow into the tree.
Also, before you suggest, between the trees is big enough to run through.
I understand if this forced movement is on a cheaper, lesser quality horse, but on my Arabian with superior handling, this "move-assist" should be disabled or at least greatly lowered. Everyone knows player judgement is usually better than number generators and therefore "superior" handling should mean complete player autonomy where movement is concerned.
If I'm wrong about the handling class of these horses, then oops, but my argument is still valid: I shouldn't have to fight my horse to go where I want it to, especially while fully bonded.
Also, horses could have varying degrees of handling that can be improved to some extent as you bond.