For the dressage potion, button braids are the "proper" thing to do, no matter what color the horse is. (There are some breed exceptions).
That being said, for lower level shows you're OK doing whatever you want (even leaving it down) as long as it looks neat. I LOVE my horse's long (but not thick) mane and would never cut it to do button braids, so I do a running braid. (I keep his mane in a running braid at home, too, otherwise it turns into dreadlocks!) Because I do it so often, I've gotten pretty good at it and it will stay in for more than a week only getting a little fuzzy looking at the top where the shortest hairs pop out. Practice is definitely the key to a good running braid!