Now I am of the personal belief that a horse should not wear leg protection for support on a regular basis. Providing constant support to a horse's legs gives the leg no reason to develop strength of its own. Instead, developing a horse (and thus its legs) slowly and gradually over time allows for the horse itself to build up the strength necessary for its given career.
Protection, however, is another matter. When doing lateral work in dressage, spins in reining, or engaging in activities such as jumping, a horse may be prone to injuring itself, and in those cases protective leg wear may be necessary. A young horse may be particularly at risk of injury since they are still learning to balance themselves and handle their feet as well as the added weight of the rider (nevermind their own weight). On the other hand however, personally I will not put protective leg wear on a horse right away. I want them to learn to pick up their feet over a jump, to learn to negotiate their feet over rough terrain, or to move their feet efficiently while doing dressage. That is only accomplished through experience - a few bumps and bruises included. On that note though, all our horses are barefoot, and so their risk of injury is substantially lower than a horse who is shod. Also, I will add protective wear if/once I feel a horse has learned how to handle his feet sufficiently. As I said though, this is all just my personal opinion based on my own research and experience.
(Bonus: you even get a glimpse of how to wrap correctly, courtesy of the photo above - booya!)