that’s not quite how that works. even at a gallop, you’re more moving with the horse than being rattled by it, and carts/carriages/etc. had suspensions to make the ride smooth (mostly for the rougher, unpaved roads).
even then, CTE is believed to be caused by multiple, sustained impacts/shocks of a magnitude greater than what one would experience while riding a horse. speaking from personal experience, none of my horse-riding (or even carriage- or cart-riding) ever came close to being hit by an NFL lineman at full-speed or being on a bombing range.