Thanks, Jackie, for your list. Here's what I found on MW that does include Nancy's spelling of cornette:

Etymology: Middle French cornette, from corne horn (from Latin cornu) + -ette
1 also cornette a : a woman's cap or headdress varying in style from the 15th through the 18th centuries and usually made of delicate materials with lappets of lace or ribbon b : a lappet of such a headdress

I would expect that although the name of the originally horn-shaped hat of these three centuries with its various styles fell largely out of use, the specific term for the sisters' headpiece remained because it is such a--to say the least--distinctive bit of headgear.

Hats are very common among women in the South anymore unless for very festive occasions, such as your own derby, J. In the North I'd expect hats to be more commonly seen because of the weather.