Punishment is a very tough and confusing topic, especially when it comes to prey animals like the horse that are so easily frightened, so let me see if I can get it clarified a bit for you.
In behaviorism (BF Skinner is the founding father of the behaviorist school in Psychology), punishment is anything that reduces a behavior by the application of an adverse stimulus after the event.
So, if I’m a test subject and press a lever and get a shock instead of a M&M, I will stop pressing that lever. This is an example of a so-called positive (just to get everyone thoroughly confused) punishment because the aversive stimulus (i.e. the shock) is added (hence positive in the sense of addition). If, on the other hand, I have a pile of M&Ms and every time I press the lever, a M&M is removed, that is a negative punishment because something is subtracted, taken away. Both of these punishments are different from aversive stimuli, such as the dinging in your car when you forget to put on your seat belt. It’s annoying so you backle up your seat belt to get it to stop. Aversive stimuli are often mistaken for punishment.
So, for example a horse gets struck after balking at a jump, that is positive punishment. Striking a horse on the way towards a jump, i.e. to get him to accelerate into the jump is not so much punishment as it is an aversive stimulus; i.e., by striking the horse, I am encouraging him to flee so he picks up speed, much like you see jockeys do during a race when they are whipping the horse back and forth with their crops to get the maximum push from their mounts and the horses are running at top speed to get away from the swats with the crop (i.e. the horses are fleeing to try to make the aversive stimulus stop; i.e. like making the seatbell warning stop).
I would be apprehensive about striking a horse as he’s getting ready to take a jump because you want to reward the horse for taking the jump,not punish him for going towards it. The way a lot of trainers and riders do it is they “spank” the horse as it heads into the jump and then reward (stroke) the horse after the jump. The theory is that the horse will be anxious to avoid the spank by launching itself into the jump and looking for the reward from his rider after the jump.
I believe it is best to get the horse to thoroughly enjoy jumping and the feeling of suceeding at jumps and the praise and affection that comes from a well-executed jump than to mix the horse up with confusing swats with a crop. Leave the crop out of it. In fact, leave it at home.