There are a good many pictures of St. Mary Magdalene as a hermit. You primarily get her as an old woman who’s spent her life in repentance, or as a woman wandering around naked and clothed only by her hair (which is shown as having grown long enough to completely cover her, or to have turned into a big haircloth garment).
Both of these images are referring to actual though extreme practices of the earliest desert monks, sisters, and male and female hermits/eremites. (It’s a lot easier to be a ragged or even naked hermit if you live in someplace warm, like Egypt. Although it would get pretty cold at night!) Legend says that Mary Magdalene emigrated to what today is France (and Gaul was the site of some very early Christian communities), and then went out into the French wilderness and lived in a cave for the rest of her life. (This is a version in which the Magdalene = Mary of Bethany. So the Bethany siblings also migrated to Gaul; Lazarus did cool miracles and led the community, and Martha tamed the dragon Tarrasque.)
I don’t think I’ve run across any legends where Mary Magdalene was deliberately ruining her looks. That’s a motif largely limited to legends of virgin martyrs, or girls who want to run away to the desert without being pursued by annoying suitors. Often their looks are miraculously restored after people quit bugging them, or immediately after death.