To keep warm. In addition to protecting the skin, hats with face coverings also helped to keep women warm in cold weather. This was especially important for women who lived in northern climates, where the winters could be very harsh.
To make a fashion statement. Hats with face coverings were also a way for women to express their personal style. There were many different styles of hats available, each with its own unique look. Women could choose a hat that complemented their outfit and made them feel confident.
To hide their identity. In some cases, women wore hats with face coverings to hide their identity. This could be for a number of reasons, such as to avoid being recognized by someone they didn't want to see, or to protect themselves from being attacked.