Unlike at least one other theme park in Orlando, Disney doesn't have a weather-specific policy. If it rains, it rains and in Florida, when it rains, it will pour.
Yes, Disney will close its magical gates when there is a hurricane and it will do everything they can to accommodate date-specific passes and tickets but for the most part, if bad weather rolls in, you have to deal with it, and guess what? That is a great thing to "deal with".
I don't know how many times I have visited a Disney World park and woke up to find out that it was going to rain all day long. O.k. it doesn't happen that much because I keep track of the weather in the days leading up to my arrival.
Still, when you open the curtains to your hotel and see, rain, dark clouds, thunder, and even lightning, it might put a damper on your plans. It shouldn't, rain can be your best friend.
It does go without saying that when the rain falls down outdoor rides close up until lightning is out of the area and sometimes, mostly in the spring, all-day rain means those rides stay closed. Luckily, many of the Disney attractions are indoors and that means you get a reprieve, albeit a wet one from the soaking outside.
My wife and I keep a packed bag in our car with rain ponchos just in case of that big afternoon shower. But we find that the rain provides a lot of relief from the sun and the crowded parks.
When the big storm begins, the parks more often than not start to clear out and that means less traffic for those sticking it out and walking around. Nothing like strollers covered with plastic bags and small tarps.
Personally, I love it when it rains and all three of my sons look at it as an advantage to jump on a bus, monorail, or a boat and head over to the park when it starts to downpour.
Rain shouldn't be a deterrent for you visiting the parks. It should be embraced. Yeah, being wet kind of sucks but watching everyone run for cover or leave the park entirely only serves to give you more flexibility and enjoyment.
Plan ahead for bad weather. When you know it might rain or know it is raining, forget the tennis shoes and hit the parks in sandals or for the kids, rain boots. Take the ponchos, take small umbrellas, or stand in the rain like my boys do and smile.
There is so many things to do at a Disney World park that you don't need clear skies. Instead of leaving or running for cover (where there is no lightning) try singing in the rain and get a lot more enjoyment.