Hag is generally used for females, but what about males? Is there a male counterpart to this term?
My current understanding of the word is: an old woman who is disgruntled, a possible recluse, and has some form of bad hygiene.
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There are many more terms for ugly women than there are for ugly men -- which seems quite unfair to me. But I found a few:
Troll - This one is probably the closest male equivalent to hag. The male troll who lives under the bridge is fairly similar to the hag who lives in the woods. Unfortunately, "troll" has taken on a completely new meaning within social media, so it might cause a little confusion if you use it in its original sense. I saw "ogre" was mentioned above. Ogres are thought of as ugly, too, but there is also a strong connotation of great physical strength (thanks to "Dungeons & Dragons" and Lord of the Rings), so it might not be suitable.
Nerd / geek / freak - These are terms to describe wimpy (and usually book-smart) and (sometimes) physically unattractive students or adults. Originally, a "geek" or a "freak" was a circus sideshow performer (for example, "the bearded lady" or "the smallest man in the world"). It was once very shameful to be considered a geek or a nerd, but today people are usually proud to be labeled as such. These terms are gender-neutral today, so they're not strictly analogous to a hag, per se.
There are terms that are more often used for men, but they can be used to refer to women as well:
(old) miser; curmudgeon; grouch; (old) codger; churl; crosspatch.
I agree that "ogre" could be a masculine word with a similar meaning to "hag", but it also has a feminine form: "ogress".
I can't think of any others, but you could look up some of these terms in a thesaurus to see whether I've missed any common ones.
I hope this might have helped you out.