Women began wearing wholesale new era hats in this manner

Wide Brims
Large hats with wide brims made a return in the '30s, following an era of brimless hats worn very close to the head. These snapback hats were often quite pliable, and women wore them many different ways, including turned up in the front and pinned with a brooch or decoration, such as flowers. In the early '30s these hats had large brims and large crowns that covered much of a woman's hair as cloche caps had done in the '20s. As the '30s progressed, the crowns of these hats grew more shallow, and the large brim sat at an angle higher on the head.
Pert Hats
Before long, smaller hats came into vogue in the '30s, and by the middle of the decade, perky hats were in style. They were similar to European sporting hats in design. They were small and sat high on the head, angling down toward the front. At their highest point they often had an embellishment that stood up, such as flowers or feathers. Sometimes they had ribbons or netting that hung down, covering the back of the head. Women often wore cheap snapback hats to show off the glamorous updos of the day.
Turbans and Snoods
Women in the '30s endeavored to look polished and pulled together at all times. With the constraints of the Great Depression being felt by many, women often could not sport styled hairdos every day. Perhaps partly because of this, turbans came into vogue by the mid '30s. Turbans allowed women to look chic without having to style their hair at all. They simply tucked their hair into the turban. Snoods also caught on in the later 1930s. They were crocheted or made of netting, and women gathered the back of their hair into them then tied them at the top of their heads.
Fedoras
Fedoras caught on and were a huge hat trend for men in the '30s. Men wore them for work and began wearing them at social occasions over more formal hats, such as top hats. Fedoras were soft and pliable but held their shape well. Before long, they caught on with women as well. Greta Garbo was one of the biggest stars of the day, and she was photographed wearing a fedora slouched down, covering one eye, a look which would become her trademark. Women began wearing wholesale new era hats in this manner, and smaller versions of fedoras were even created just for women.