There was actually a blurb on this a sociology text I read. It is a combination of cultural and sociological as well as instinctual factors.
Essentially, in cultures that prize horses more for companion animals, it tends to be females who gravitate to them because they present an opportunity to practice caring for a protector figure. Most females have, on an instinctual level, a drive to nurture something stronger than herself. This stems from a time when being able to attract and "keep happy" the best provider resulted in a safer home, more food available and stronger children. Honestly if you watch a happy couple in the "honeymoon phase" you will see in a LOT of instances the woman become more "domestic" with no prompting. In cultures where horses are viewed more as a tool for a job it tends to be a male dominated interest. This does not mean that men do not bond with their horses, it simply means that the human brain will take cultural views and apply instinctual cues to them.
And I wanted to say that this reply is very interesting and I agree with the ideas although I have never thought of them before.