Is ‘anything in a skirt” a popular idiom? Does it have special overtones?
Solution 1:
It's meant to emphasise the subject's promiscuity. In this form it is a replacement for "any woman" and carries no undertones with respect to women, with the possible exception of implying that wearing skirts is associated with women.
It is certainly not a general or neutral alternative to women in other cases. "Skirt" is often considered a derogatory term for women.
For similar figures of speech, compare "anything with a pulse", or "anything that breathes".
Solution 2:
I wouldn't use "anything in a skirt" as a plain alternative to "female" in conversation. If you're referring to grown women, use women. If you're referring to jailbait (girls not legally old enough to have sex with in most states in the USA (usually 18, except in NJ, where 13-year-old boys can legally have sex with 13-year-old girls but 18-year-old boys can't)) as well as grown women, it's probably accurate enough. If you're referring to Mel Gibson in Braveheart (all the Scots in that film wore kilts, and a kilt is a kind of pleated tartan skirt worn by men), then you're talking about something different.
The idiom is used to disparage the man being referred to, as is skirt chaser. It means that he doesn't pay attention to anything except the skirt because it's a stereotypical sign that the person wearing it has a vagina, a sexual organ that he's addicted to whether or not the owner is in any other way attractive. Put a skirt on a ewe and he'd probably try to have sexual congress with it as well.
I'd also say that calling any female a skirt is politically incorrect and demeaning these days, just as it was in the past; however, to say that "John'll jump on anything in a skirt" is probably fine in most conversations. Native English-speakers will know what you mean and are just as likely to use it without fear of offending anyone but "John".
I'd call anything in a skirt a literary as well as a conversational idiom that means something like any female (dead or alive) (but not men wearing kilts).