Thrum caps are primarily a male accessory, but we do see them in images of women working in the marketplace. Most images and references seem to be middle-aged or older women.

“A thrumbe hat had she of red, Like a bushel on her head.“
– The Cobbler of Canterbury, 1608
“She put on her fairest smocke, a petticoat of a good broad red, her gown of grey faced with buckram, and her square thrum’d hat, and before her hung a clean white apron.“
– Dobson’s Drie Bobbes, 1607

There are also examples of women wearing thrum caps when drunk or disguised as men. In these cases, they’re wearing male-coded variants such as the blue skullcap.
