Great question! First time I've seen this topic here.
The sweat-on-the-face thing is only a problem for me during the summer, which is a hot and humid time in Mississippi. Usually I just wipe my face with my singlet, but especially in runs lasting over an hour, that's not much of a solution, since the shirt, even when stripped off and squeezed out, is still damp-to-wet and doesn't absorb much.
Recently I've taken to running 8 miles on a closed 1.5 mile loop in a park, and for the first time, I station not just water bottles but a big beach towel at the spot where I stop at 3, 4.5, and 6 miles. Drink first, then wipe off the face, head, hands. That works.