The same was true in most of Europe until there was good reliable heat. All eastern women in the old movies made to report events in the thirties and forties show women in headscarves
Nuns still wear head coverings, real tight full head coverings
pioneer American women wore various bonnets as head coverings
Any of the places you listed have “morals police” that will arrest the “uncovered” woman?
Any of these places will have people throw acid into the faces of the “uncovered” woman?
Some Christian churches still require or encourage a woman’s hair to be “covered” during services. Black churches especially seem to be fond of the “church hat” phenomenon.