I personally never really understood the whole body and pubic hair thing. I hate seeing it. I personally get rid of mine and the characters I draw are also clean shaven, although most of the characters express massive amounts of sexuality.
I think the whole long hair thing on women comes from the classic gender roles. Women are to stay at home with the children. This fits the description of supportive, obedient, kind and nurturing. Why long hair? Any active person would know long hair really gets in the way of things. It requires a lot of care; care that an at-home woman can handle but an active one would have a hard time with. I used to have long hair but I couldn't keep up with it and I thought it looked fucking stupid, so I cut it. I was in many activities and didn't have time to wash it every day, I hated combing it because it was a big pain in the ass to do, my dog would sit on it at night, I couldn't wear hoodies, it got caught in everything including my backpack, and I was into fighting and it would always be pulled and used against me. Not fun. It also gave me headaches. After I cut it, it was quite the weight off my shoulders. Unfortunately, many people saw me differently after that. You're right, short haired girls are portrayed as strange or mean so that social stigma stuck. I am very strange, so it went well with my personality there, but I am by no means mean. Back to gender roles, it is expected of a woman to be subservient. One that doesn't conform to those standards is considered strange, and being independent could come off as mean. Many strong, independent women have short hair, so the misunderstood stereotype stuck.
In Asia men used to always have long hair as well as women, it was a sign of well-being, status, beauty and pride. Somewher along the course of history the Europeans decided short hair was the thing and spread it around and somehow it stuck although slowly the stereotype is being broken as we see more celebrities like Emma Watson cutting their hair and she's not a symbol of cruelty, evilness, or creepyness at all. And with the whole emo phase hitting teenagers more guys are growing their hair too.
At least that's a miz of what I've learned and observed. Personally I dig guys with long hair though
I don't think there is any objective correllation. It seems these things are rather arbitrary and mercurial; artefacts of the culture that produced them. The Masai people of East Africa seem to be rather fond of bald women, for example. What's more, I think shorter hair was preferred on women in the earlier half of the 20th century. Looking at media from that era, it certainly seems more common.
Anyway, if you see it in fictional settings, it's just the result of lazy worldbuilding, with the writer simply projecting a melange of Western cultural perceptions onto the characters.