What everyone else said.... I recommend dressage to anyone in ANY discipline since it teaches horse and rider how to communicate and how to move together in a balanced way. The way a horse naturally moves at liberty, with the exception of those odd moments in play or flight where it collects itself, is not the healthiest way for it to carry a backpack weighing well over 100lbs. To carry a rider in the most balanced, and indeed safest way possible (in terms of long term soundness), the horse pushes itself forward with its rear end, since the hind legs are far more powerful than the forelegs and better able to take the weight. The horse also needs to lift its back using its abdominal muscles, which allows it to properly use its back muscles to handle the weight of the rider and also lets the thrust of the hind end come through. That, in a nutshell, is what dressage does and teaching a horse to move in that way is incredibly beneficial regardless of discipline.
And it doesn't matter a hoot what the rider is wearing in order to train this stuff. I usually slum it when I go to the barn and wear all the manky t-shirts, hoodies, etc. that I might not (er... "might" being the operative word there) wear to the pub.
If those of you who worry about this sort of thing are lucky, I won't ever show up at your barn. When I was at a stable where people cared deeply about appearance and prioritized looking "neat," I discovered the joy of tacky saddle pads; you know, the ones with flamingos, fish, flames, NYC subway graffiti (I'm not kidding), tie-dye, rainbows, sparklyness, tiger stripes, stars, swirling galaxies, etc. etc. Then I upped my game when I discovered one could acquire equally as garish polo wraps (about the only use I ever found for the things) and if you get a few sets of those, you can mix and match them so you in fact can have four different polo wraps on your horse with a saddle pad that doesn't match any of them. Absolutely brilliant!
Now that I've gotten older and lazier I've stopped being bothered with the polo wraps but am proud to say that I don't have a single solid coloured, much less white, saddle pad to my name.