I'm going to my first lesson pretty soon, but wouldn't it look weird to see a guy bouncing up and down on a horse in a very proper manner?
If you look at the upper level showjumpers, the majority are male, most that spring to mind are men, the Whitakers (bar Ellen), Tim Stockdale, Nick Skelton, Ben Mayer, Scott Brash, William Funnell. These are the top riders in the industry, and most are men.
If polo is what you are interested in, it is dominated
by men, as it was played by soldiers in India, where it was then brought back to Britain. Here in England, I would be more surprised to see a girl on a polo team than I would be to see a guy on a horse.
If it eases your worries, I work at a riding stables in the holidays, and we recently had to young lads (late teens/early twenties) take up riding, and they love it. It can be intimidating at first as yards tend to be dominated by young girls, but they won't bat an eyelid at seeing a guy turn up - and hey, you never know, you might meet a girl! Why most of the lads I know who go to shows do so, for all the girls