Do you see that Musqueteer hat that made it to the Renegades of the Wild Wild West like of that fella and is actually a technology upgrade of that one Gentlemen from the Dollar notes? Washington and his Crew were not wearing it when it rained all closed up with buttons, but exactly like the others.
The point is the material used to create a rim being flexible yet stiff enough to stay in shape when it rains or storms or be put out of eyesight when sun cover for the eyes was not needed, but visibility. That's why on all war paintings the Fedora is shown as a Triangle hat. Only in real heavy rain the hat was useless, but just like everything else than a rooftop. With understanding how to stiffen leather the buttons went away and the modern Fedora shape was created and worn until the invention of Baseball Caps, I guess.
:-)
