I find that my skin is quite naturally waterproof :-)
seriously though, I do get too hot in proper waterproof stuff, doesn't let me breathe enough. I prefer to run in the dri-fit type stuff which doesn't get too soggy, and dries out fairly quick when the showers stop. Also a baseball cap keeps most of it out of your face.
I've just come back from a 50 min run in the rain and it was lurvely (though I'm sure I wouldn't be so keen in the middle of winter!)