I'd also suggest going to a runners' equipment store and checking out those hats. They've got a lot of them with very long visors that provide full, excellent coverage, lightweight synthetic materials that fit under helmets nicely and don't hold water, are constructed with low, unmolded crowns, and that are breatheable, for comfort.

Additionally, I carry a handkerchief in my pocket to wipe off my glasses when I arrive at my destination.

Last winter I began using a Dux Helm helmet which has an integrated, retractable visor lens that covers the eyeglasses. This worked excellently at keeping my glasses clear, and although the Dux Helm lens obviously got wet, it was much more comfortable looking through the drops with good vision rather than with the blur of my astigmatism uncorrected.

The trick with the Dux is to have eyeglasses with a wrap style frame; there's not a lot a space behind the lens for most face shapes, I suppose. Works well for me, though.