It is common here for men to have short hair and women to have long hair, but not unusual to be reversed. I know lots of women with short hair and a few men with long hair. I think it is cultural, for sure, but I have no idea where it started. 

One interesting thing I have noticed is that men who work in white collar jobs, for example, finance, business, engineering, etc. mostly have short hair or are bald anyway. (long hair and baldness on a man is usually not a good look for men here). It doesn't matter as much for women in white collar work what their hair style is, but I think the majority still follow the social norm of having long hair. 

There's an interesting article on why women are associated with long hair: http://time.com/4348252/history-long-hair/.

But as I said, it's cultural. There are cultures where the majority or all men have long hair. Male Sikh don't cut their hair bit wear a turban. Also, male Rastafari often wear their hair in long dreadlocks.