I was going to guess it was their big, broad shoulders. I used to have Arabians and their legs just sort of went forward/backward when they walked.
But I find Quarter Horses have big, broad, undulating shoulders. Is that what you are feeling, large undulating shoulder movement?
The weirdest, most undulating walk I have ever felt was a TWH mare. I thought she was lame for the first few minutes. She really walked like a camel. I don't mean all gaited horses either, because I now own one and have ridden a dozen others. But this one TWH was weird!
But my personal observation has been that the more muscular the horse, the more you feel their shoulders.