If it's sweat blowing upward from the face, I'd agree with Doc I. Try a few days growth of beard. Doesn't take much for the evaporative cooling effect. In winter I usually let mine grow out more but in summer I'll keep it shorter. Still works.

I noticed this years ago when I shaved my legs and arms for racing. It felt weird, clammy like my skin wasn't evaporating properly anymore. I don't have very hairy arms or legs and I notice it doesn't take much to feel more comfortable due to that evaporative effect.

There are also sun protection face masks of wicking fabric for active folks who don't want to wear sunscreen or need extra protection. An ultra thin bit of mesh wicking fabric might do the trick below the eyes without interfering with breathing. Or if you already have a bandanna or bit of thin cloth around, try it on one or two rides and see if it helps. I wear paper dust/surgical masks for rides on very cold dry days and it hasn't interfered with my breathing on moderate effort rides. And those masks don't wick very well -- when they get saturated with moisture from breath they tend to clog up and need to be replaced.