Grandmother had some interesting older hats that she let me wear to play, along with some vintage style dresses with vintage fabrics - dimity, matelase, viscose, jersey, and rayon.
Women's hats could be annoying if you were sitting behind someone with a broad brim at church or a movie. Unless women came to a function and started working, such as serving food at a covered dish luncheon, they rarely took their hats off.
We even wore swim caps when going to the beach, lake, or a pool. I liked one that had brightly colored dimensional floppy flowers, but the caps pulled your hair painfully when taking them off. They kept your hair dry but wouldn't protect any specially styled coif.
Because we lived in sunny Florida, wearing a hat for protection was always acceptable. And of course the men wore hats during hunting adventures.
"...a woman should cover her head." 1 Corinthians 11:6