What do you call a horse riding event dress down up or dressage?

The term you're looking for is dressage.

Here's why:

* Dressage is a highly disciplined form of horse riding where the horse and rider perform a series of predetermined movements in a specific arena. It emphasizes precision, elegance, and the horse's responsiveness to the rider's aids.

* Dress down and dress up are informal terms referring to lowering or raising the formality of attire, not specific types of horse riding events.

Let me know if you have other questions about horse riding or dressage!