As someone who has been to Disney during 3 hurricanes.... you put on one of the numerouse ponchose you own (yes, believe it or not, sometimes I forget to pack them, and have to buy new ones). I now bring them all, just in case one of them rips.
We also own, Universal and Seaworld ponchos! LOL
As long as the weather is warm, put on your shorts, t-shirt (Not white), or wear your bathinsuit too. Wear water shoes or sandels, they are better than squishing around in wet sneakers!
You also don't mind getting wet on SPLASH MOUNTAIN!!!