I agree with the comments about position on the bike. Back when I was racing and also doing endurance events, I don't recall having to wipe sweat out of my eyes or face that much. Perhaps somewhat on a long climb on a hot day, but other than that it wasn't a huge issue.

I'm also a competitive horse rider and am almost always in a very upright position. With horse riding, I do find that I'm constantly wiping sweat off my face because otherwise it goes into my eyes.