I bought a Halo head band for my perpetually un-prepared DH last year. He does not like heat, and he loses a lot of salt too. I think it worked pretty well, since he wore it all through a three-day ride and it would leave a silly imprint on his forehead.

Or you could make regular stops, wash your face, dab your eyes with fresh water, and re-apply your sunscreen. If you want to save all your water for drinking, you can get some nice pre-moistened facial wipes at the drug store.