Every sport has its silly-looking costumes. Would any man wear something like this?
Equestrian http://t1.gstatic.com/images?q=tbn:ANd9GcT6-ZWqWHW8V6LDlBujbH9RvQj4txPzf53ct9hR1qMQ1s-wo-4d
Golf http://heritage-classic-golf.com/images/orig/heritage-classic-golf.com/golf-fashion-stewart.jpg
U.S. football https://encrypted-tbn2.gstatic.com/...5XwAs5IR2QovQzsq9fIJOsaQ7oSOz6ofIgthHjshQXIhw
Basketball http://blacksportsonline.com/home/wp-content/uploads/2013/08/NBA-Short-Shorts.jpg
Edited to add: Actually, that red coat is kind of cool. I think I might wear that, if i could find the boots.
The guy in a red clothe is not really dressed to compete in an equestrian competition. It is more of a traditional costume.
Here are the medalists in show jumping: http://www.horsejunkiesunited.com/wp-content/uploads/2012/08/1-medals-w1-all-teams.jpg
dressage: http://www.horse-today.de/wp-content/uploads/2012/08/duJardinC_Olym12ss_4563-601x399.jpg
I compete in dressage. I like the classic outfit. It's very classy. The only issue is that wool coats are way too hot during the summer. For training, I always wear sportswear likee the one I use for running etc....