It’s not a Hungarian specific minhag, nor is it related to pogroms and women being violated, rachmono litzlon. Married women shaving their heads is a takana from the Vaad HaArba Aratzos from 500 or so years ago, due to concerns of chatzitza and women’s hair being completely covered, as explained in the Zohar HaKodosh Chelek Gimel, 256a, plain Zohar not Raya Meheimna that one strand of a woman’s hair being revealed is a great tragedy and brings destruction to herself and those around her, bringing connection to Lil-.
Amazing how all the experts here on minhagim and the reason why chassidish women shave their heads seem to base their entire reasoning why it was or wasn’t a thing on external violence being applied to Klal Yisroel, and photographs from well after the beginning of the Haskalah, which led to the change of countless ancient minhagim outside of very chassidish circles. Women in all lands governed by the Vaad followed this takanah, including Poland, Lita, Hungary, Bukovina, Ukraine, and Russia. I know also a Sefardi talmid chochom and mekubal whose wife shaves her head al pi Kabbalah. Though there is this Ari in Shaar HaMitzvos addressing why women should perhaps keep their hair, the Zohar in Chelek Gimel, can’t recall daf at this time, states that women must cut off the hair and fingernails that grew during the yemei niddah, which l’maaseh would be accomplished by shaving the head since hair grows from the roots and not from the ends of your hair. Maybe the oilem here should spend more time learning and doing proper research into the mekoros for our minhagim hakedoshim rather than just shmeesen in the kave shtibl.