Okay, now to answer about men in general. I am sure most men will not, I said most men and not all men, yes there will be some men who might date a woman with short hair but most of the men will not prefer that.
Coming to me, if you ask me then I would say I am an outright exception in this case, because I absolutely find short/boy cut/pixie cut hair on a woman very appealing and attractive and unlike other men I absolutely dislike long hair on women and it totally puts me off. Hence if the woman has short/boy cut hair then that will certainly be appealing to me.
However the answer to your question is "NO", I will not date a woman who has short/boy cut hairstyle. The reason for that is " I never want to be in a relationship". I have decided to stay single for my lifetime.
However I would certainly want to be friends with her, even best friends, of course with her consent and only if she doesn't mind. That itself is enough for me.
It's that in many cases women simply look less attractive with shorter hair. So if she's really gorgeous with a crummy haircut, she's still pretty attractive. If she was borderline, could drop her into... n'ah range.
Is this always the case?
For petite, slim women i actually quite length chin length or even slightly shorter hair, if it's a good hair style. It can be as hot or hotter than some long hair styles on that frame.
Really short hair, to me, pretty much always looks significantly worse, and if she's not very feminine in features, build and makeup, looks terrible.