Here are two of the hats that i wear on the field, depending on how hot it is:
The first is my tricorn hat that is made from a wool blank that can be purchased from Jas townsend. I added the trim and molded it myself.

Next is my half cocked hat that i've had since my earlier days reenacting. I use it when the sun is horrendous and it kept me from turning into one giant blister at Rag. It is also made of wool. I am the one bending over to pick up arrows in the black and white with the barrel on my back

I saw Rap say that straw hats are going to be banned next year?
If this is true, then might i recommend reading the article i post below and reconsider for it is clear that they are indeed period.
But if this issue has already been resolved, then i apologize for kicking a dead horse topic.
http://www.larsdatter.com/strawhats.htm