Equestrian sports are one of the few sports that do not have different divisions for the genders. Men and women compete on equal footing in all the Olympic equestrian disciplines, e.g.. I'm sure announcers and such may casually refer as they wish to a "gentleman" or a "man" or a "lady" or a "woman," but generally there's no formal "men's division" or what have you.
Of course, there might be occasional classes at a horse show that would be for one or the other, and I'd guess they would refer to "ladies" or "gentlemen," but that would be rare, and I'm only guessing. But probably they would use "ladies" and "gentlemen."
However, if you are the Master of Foxhounds of a hunt club, you are simply "Master" at all times, be you man or woman.