Taken from the book, “Adorned with Dignity”
There are many sources that state clearly that the women wore wigs in the Gemara’s times in order to beautify themselves for their husbands in their homes. In those times (before the warning the Zohar) woman wore their hair in the house. Those who had thin or white hair wore sheitels in order to look nicer for their husbands at home. When these women would go out in public, they completely covered the wig with a kerchief. (From here we see that the wig was worn as a substitute for hair, not as a substitute for a head covering.) רש”י ערכין ז, תוספות ריד והנמוקי יוסף בשבת סד, מהאגור בסימן תל”ו, דברי רבינו ירוחם והטוש”ע א”ח סימן שג’ סעיף יח’.
The following is a proof that in the רשות הרבים the women who wore wigs completely covered them with a kerchief:
There is a halacha that a woman may not wear a wig in the רשות הרבים (this is referring to the רשות הרבים in the Gemara’s times) for fear that she might take it off and show it off to her friends which would constitute carrying on Shabbos. If, as you said, that the women wore a wig in public as a head covering, it wouldn’t enter someone’s mind that a Torah observant woman would take off her wig in public and display her hair. From here it is clear that a woman would completely cover her wig with a kerchief and the Chachamim were afraid that she would take out her wig from under the kerchief and show it to her friends.
It was so self-understood that a married woman would cover her hair in public, that even the secular women would cover their hair. See Rashi Sanhedrin 58:2 – שהיו רגילות את הנכריות שלא לצאת בראש פרוע – As is seen in history books.