I disagree with buying a mickey poncho. You'll see thousands of yellow mickey ponchos and if you have the hood up, it's hard to keep track of who is who. My wife and I bring clear ponchos, much easier to keep track of eachother.
It rained pretty hard, I think it was Christmas day last year when we were there. We went to the Magic Kingdom and rode Splash Mountain about 5-6 times in a row with no line. We also hit Space Mountain as well.
Go to your favorite park is what I would say, because the lines get shorter when it rains because people go back to their hotel room. Also, we hit the rides when there are parades for the same reason.