What happens if you're in one of the theme parks during a rain storm? Watch droves of people leave for the day!
My advice is DON'T LEAVE! The one thing about the rain in Florida is that, sure it rains several inches in an hour, BUT it stops after about an hour! The water is quickly drained away and the park is a lot less crowded. Unless you live there or visit often, you wouldn't know that.
Now what about hurricanes? The good thing about Orlando is it's in the middle of the state and It's far enough away from either of the oceans that it isn't effected as much by a hurricane. It will rain heavily and the park will be almost empty!
There have been exceptions to this. A few years, a hurricane did a lot of damage around the Walt Disney World area. I know that one of the hotels in Downtown Disney was so badly damaged that they had to close.
My family and I actually were vacationing when a hurricane started. Instead of staying in our hotel room all day, we went to the Magic Kingdom! We got really wet and we didn't bring any ponchos with us. So, I went to the Disney Emporium and didn't see any rain gear, so I asked the cashier if they had any ponchos. She said that they did! They're kept behind the register!
It's a good idea that you bring an extra set of clothes with you in the summer. In all of the parks, you can keep clothes, rain jackets, or anything else that you don't want to carry around with you in a locker that you can rent. The lockers at the Magic Kingdom are located just after you go through the turnstiles on the right. The wheelchair and stroller rentals are located at the same place.
A word of warning, you should bring a light jacket or sweater to Florida in the summer. It's very humid and it can get a little cool in the evening.