John's hat is a darker greenish olive of rabbit fur felt. This is pretty good in cool weather and is okay in light rain too. Mine is the khaki one in canvas duck that came from Orvis. It needed modifying by covering the silly leather hat band with a strip of material, webbing in my case, so damp flies can be stuck into it. That way they do not bring water into the fly boxes and rust all that hard work away...
This hat has been superceded at Orvis by the River Guide Hat and sports a reinforced brim so you can shape it. My advice would be to keep it shaped like an upside down dish to get the maximum shading effect for your polarised spec's.
You may like to obtain several hats to cope with the vagaries of weather, a dark green or brown straw hat maybe, for boiling hot days in summer; one of canvas duck for most days and maybe something waterproof, or at least water resistant for rainy days. Just make sure that whatever you get, your hats should shade the back of your polaroids as well as the top and, most importantly, they are always as drab as you can get.
Well that's your head taken care of. Next time trousers and how they also contribute to observation and stealth!