In the US, tails aren't usually braided for dressage-only shows b/c the braid might influence the way the horse carries its tail, etc.

You see it sometimes during dressage at eventing shows. I personally really prefer the look of a braided tail to one that is shaved. I HATED having to shave Baxter's tail this summer.

...and I whispered to the horse; trust no man in whose eye you don't see yourself reflected as an equal.
-Don Vincenzo Giobbe circa 1700