I came across a photo of some Welsh woman having tea that dates to 1910. The hats are odd enough that I asked a fashion savvy friend (Jheri) for information. She found a museum link and added that a shorter more conical variation is still worn to celebrate St David's Day on March 1st.
Jheri is a big fan of hats in general and notes they are making a comeback among 20 somethings - although hats like this are probably a bit of a stretch. On the other hand, if they were used as a space to carry a lightweight deployable umbrella or perhaps if they were covered by solar cells for charging electronic kit... :-) Or perhaps just very odd fashion.