There are Sefardish seforim that pasken that married and unmarried women must wear a full head covering (that leaves only the face visible.)
As I’ve pointed out to LUL elsewhere, Rav Vosner and some Achronim are Choshesh for the Magen Avraham and Rashi, and hold that a woman has to have her hair braided, whether there is a requirement of covering (i.e. under the covering) or not.