Besides coming from a western working horse background, I've had long association with hunters/jumpers AND the 3 day event/sport horse industries.
I appreciated (was really "tickled") seeing the hunter (& jumper) minis/ponies at both Congress and Nationals (and the handful of other rated shows that I've been able to go to) that were shown in an English style headstall with a lead and with their manes and tails properly braided (I like it in the lead line classes, too). WOW - that was over and above the rest and I just LOVED it!!! While not necessary, especially braiding in Jumpers, it's just really cool to me and creates a lot of appreciation for that particular horse/farm/handler - no matter how/where they placed.
I know that when I do show in those events (my goal someday - Looks to be TOO MUCH FUN), mine will be shown just like Hunters in miniature (I also LOVE the presentation/picture from TargetsMom - Mary) for the hunter/jumper classes (western style in halter obstacle)... Then I'd also have to find clothing that represented the hunter disciplines as well ... hmmm... That may be harder to do (my size) and also harder to compete a jumping horse in while running on foot! Sport horses used to be presented in hand with tan or white pants, a belt, a polo shirt (could be in farm colors but not with the farm emblem), with hair contained but not necessarily with a hat on and some type of running shoes (usually paddock boots, but I have seen actual running shoes & some of those folks have to RUN to present their big, long strided, trotting horses). I'm not sure if that is still the norm for Sport Horse presentation...