And again on the women and scarves thing, it's in the bible actually + I can imagine it's helpful for keeping warm and keeping your hair out of your face when working outdoors. I think they would have felt a bit naked and very forward to walk around with their heads uncovered. Even my grandmother wore a hat or scarf a lot of the time.
Soviet women probably never read Bible or visited a church. Nevertheless, their mothers did. It was just a tradition. Besides, a scarf helps to protect your hair when you work outdoors.