My horse gets bathed before shows (we go to ~3 per year), and spot cleaned every day that he's there. He stays surprisingly clean at home, but when we go somewhere else, he likes to poo in the middle of the stall and sleep in it
I shampoo before braiding and don't have any problems with it, but I only do a running braid because his mane is so long and I'm not willing to cut it to do button braids. You could put a little gel into the braids if you have problems with them coming undone. (I guess then you'd need to wash your horse after
the show, too!)
I also hose him down any time he gets sweaty during a ride.