What is the purpose of dressage wraps?

Dressage wraps are the same thing as polos. I have never really heard of a difference. Yes, dressage movements are obviously much less "obviously dangerous" than jumping or doing barrel racing, but there is always a danger of a horse knocking itself or banging their legs, especially when you are asking for extensions or collections. Also, when you do flying changes, piaffe and passage there is a chance of a horse hurting themselves. Most dressage riders use polos as a way of supporting horses tendons as well, and when doing more advanced movements or long schooling sessions I am sure that even the horse appreciates the support. Like going for a run in new nikes verses flip-flops? I have never heard of a rider using wraps for warmth as a sole reason.

Plus, most dressage horses look pretty stunning when they are in clean black tack and spotless wraps and pads.

Haha... Dressage movements do require support, actually. A lot of it. Sure, dressage horses don't land hard like jumpers and don't slide or spin like reining horses, but lots of stress goes on those ligaments and tendons during various movements. You're probably thinking of training level tests. Those hardly require protection of any kind. But after that, it's definitely important to protect.

Dressage wraps are the same as a polo wrap. Therefore, they support the ligaments and tendons in the same productive way that a polo wrap does.

How is a piaffe safe without leg protection?

give support. All those dressage movements are, like any other discpline, hard on the horses tendons and ligaments. The extra support/ shock absorption helps take the shock off the tendons.

Polo's are good for keeping the tendons warm. (: That's all the I know about polo's really and their use. They also produce a nice professional look.

Perhaps to keep their legs warm so they don't pull a tendon or get too sore. That's why ballerinas wore leg warmers for warm ups.