That might apply to local levels but when you get to the world shows, etc in AQHA, ApHC and others, most of the big name trainers and show people are men. Big bucks in it. Lot of people buy a horse, turn it over to a trainer and do nothing but bask is the recognition of being the owner :)
There's a lot of men in Arab shows... they're still often gay... with the exception of Patrick Swayzee (I think)