Majority or not - it's definitely an equal platform for all riders - everyone is marked/scored/given the same course as eachother.
I do believe as a majority, men have more guts then women, which seems to be why men are seen more at the highest levels at say eventing or showjumping - but then you get a breezie madden and she's got guts of steel.
Men are also bigger as a general rule, so they can manipulate and push around the horses "easier". But these days you can train them so well they don't need pushing around.
Yes. In all honesty women have to work less then men to be good because this is now a female dominated sport. People like Tj O Mara have to prove that they are actually good. He won the Macau because be jumped a majority of his jumps on the counter lead. Brianna Goutal just took out strides.