There is absolutlely a difference between men and women though, in equestrian sports.
Firstly, male competitors are overrepresented compared to the overall proportion of boys and men who ride - at my yard, for instance, there is one man, compared to maybe 25-30 women and a few girls. I have always assumed this is because men are more competitive by nature, and possibly braver, so more likely to want to compete at high levels in a dangerous sport. Perhaps sponsorship is also a factor in some disciplines, given the expense of equestrian sports, plus of course it is very time-consuming, which can be difficult for mothers.
But maybe there's more to it. A couple of articles:
One from the US
Men dominate the Olympic equestrian podium although only 25% of participants overall are male. In the last 4 Summer Olympics 11 of the 12 Show jumping medals won have been by male riders
And another
men win far more individual medals than women at the Olympic Games across all [equestrian] disciplines. In some cases, the disparity is staggering.... in Show Jumping Twenty-five male riders have taken home individual gold since 1900 – women’s participation began in 1956 – but no woman competitor ever has.