This is one of those questions that's sorta goes, "I get sunburned when I'm out in the sun. How can I prevent that?" By taking preventive steps, that's how.
So, on the one hand, I see your point a little sun in the face is a nice thing (besides, now reports say too little sun can be bad for your health, too). But, you get sweaty, and sweat runs into your eyes, which of course can be annoying.
What to do? One alternative: Slather your forehead with antiperspirant. I'm not entirely joking the stuff works on your armpits (and your feet, if they sweat heavily). So why not your head? Two possible downsides: One, I have no idea what effect aluminum chlorhydrate, the active ingredient, might have if it gets into your eyes (although it seems pretty benign). Two, without cooling sweat, your head might overheat and explode...or something like that.
Option two: Wear a sweatband. I always wear one under climbing and cycling helmets, as otherwise I always have sweat running down my face. By itself, a sweatband makes a fashion statement that may not be exactly what you have in mind, however. Still, very effective, and if placed at a jaunty angle and combined with an eye patch, you're sure to make quite an impression on the trail.
If you're looking to make more of a street-meets-trail entrance, take a look at the multi-functional bandanas from Buff, a Spanish company that's making strides in the U.S. market. Its Original Buff ($19; www.buff.es) is a tubular piece of fabric cut to be worn for all manner of sweaty outdoor pursuits, from hiking to jogging to biking. In its corner, it's very light and can easily stuff in a pocket or pack.
Your last option is, alas, the one you reject a hat or visor. I'm partial to hats, myself, as they keep the sun off my head, reduce sunburn, and actually keep me cooler (in most cases) than sans hat. Outdoor Research's Radia Cap ($20; www.orgear.com) is ideal light, cool, and fast-drying. OK, so the brim keeps the sun off your face, but your skin will thank you. Then again, you could always just flip the hat backwards so the bill of the hat covers your neck, the sun's on your face, and you look just like every aspiring suburban hip-hopper out there...