My lesson horse has pretty big movement. I noticed when I recently rode a smaller horse with a shorter trot that I was better able to keep my hands near his mane throughout...but that horse was small enough that I didn't feel like I could get a good leg on him (I felt like with a good stretch I'd be able to rub my feet together). So the bigger horse with the bigger movement it is.
I'm at the point now where not being able to keep my hands quiet is limiting the horses I can ride, so I'm grateful for any suggestions on this!