Mary, to say that in equestrian events it`s the horse that does all the work while the rider just steers it is a way-off statement. The rider has to be able to assess every turn & approach to a jump, and issue the horse instructions through physical communication with the horse (legs, reins etc). They also have to be able to steady & slow down a sometimes over-eager horse, which can take some physical effort.
Dressage requires more precision, patience and finesse, a "softer" feel, which could be why women have the edge there.
When you get to jumping over 6ft triple-jumps and especially eventing, the fear factor comes into it as well. I think here men have the advantage, they seem to be able to deal with fear more easily, maybe it`s because we can block out the fear, or ignore the possible consequenses. I don`t know why this is, but I`d guess it`s why you find more men in sports like skydiving, paragliding, rock-climbing etc than women. It`s not that women can`t be as good as men in any of these, I think it`s that they are not prepared to take the same risks as men are.
I know some very good female paraglider pilots, they probably have a better feel for the air than most men in the sport, but most are not prepared to fly competition rated gliders, as they are more dangerous to fly than intermediate or sports gliders. In the context of sailing, that`s why more women will sail boats that they feel they can comfortably control, whereas men want to sail bigger, faster, more "on the edge" boats. In this respect I can`t see a women sailor pushing a 49er or Tornado as hard as a man would, and will take fewer risks at aggressive starts & mark roundings. Women have a higher sense of self-preservation than men, and unlike men, women can acknowledge that they are, in fact, mortal.
We`re fortunate in the sense that a mistake in sailing usually ends up in a swim, which most of us are not afraid to do once in a while.
What I`ve noticed in paragliding is that when a guy has an accident & breaks an ankle or wrist (ie a non-life threatening or paralysing accident), he can`t wait for the cast to come off so he can go flying again, (some fly with the cast !) while many women pilots, after even a bad landing where the injuries amount to some bruising or maybe a sprained ankle, tend to re-evaluate their desire to fly.
I don`t think it`s because they`re scared, I think it`s because they might just have a greater appreciation of what might have happened if the situation were a little worse.
From a personal viewpoint, my fiance broke her arm 3 times while horse-riding, and has decided that sailing with me is a bit safer ! This suits me fine since I have crew, however I know that if she is injured badly or is put into a possible life-threatening situation (like if we have to be rescued while sailing in the ocean), she might think twice about her involvement in the sport. She has tried paragliding and decided it`s not for her, while I still fly after having seen accidents that resulted in paralysis, and have lost more than one friend to the sport.
It probably is all about testosterone.

Cheers
Steve