Here's a few threads with tips on eating/drinking during a run. I had the worst problems with it last year and this year it seems somewhat better. Haven't done any long runs, but the drinking out of cups things seems to be improving. The big tip that helped was the folding of the cups tip. Then you can kind of suck it out of the cup like you do with a water bottle. I don't have a problem running and drinking out of a bottle.

Also, I wear a visor for most hot-weather runs so I find that the visor stops the water from pushing sweat into my eyes. But then, I barely sweat off my face, so not sure this would happen to me anyway.

Thread 1

Thread 2