I can't speak for horseracing in the U.K. or Europe, but here in the U.S., especially here in the western U.S., it's clear from observing horses in the wild that they truly enjoy running.
The government needs to control the numbers of wild (mostly feral) horses on public lands in the western States, and, having participated in the roundups it's truly inspiring to see the horse run in the wild. It's also clear that there is competition among many of them for being in the lead. I've friends in the horse racing business, both Quarter Horses and Thoroughbreds, and the young horses are selected for racing based in large part on their desire to compete.
The "whip", as you call it is actually a "crop". It must meet certain design characteristics and its use is strictly limited by the racing authorities. "Jockeys are forbidden to hit a horse on the head or flank and cannot use the whip during the post parade or after a race, except to control the horse. Also, whipping is penalized if it causes welts or breaks in the skin, and cannot be used when a horse is "clearly out of the race or has obtained its maximum placing." The rule defines correct use of the whip as showing the horse the whip before hitting him, using the whip in rhythm with the horse's stride and using the whip as an aid to keep a horse running straight..." (Source: The New York Times, May, 2009).
The crop is designed to produce a snapping sound when used and this is the primary motivator to the horse.
I can't speak, obviously, the the art of fox hunting from horseback. We hunt foxes here (mainly in the southern states), with especially bred fox hounds...