Hi Katy!
The best thing to do when it rains is to stay where you are! I'm serious, so many people leave the parks when it rains that when it passes (which is usually fairly quickly), the park is empty and you can pretty much walk on everything. Grab a poncho and ride it out.
If you aren't into getting a little damp, my favorite thing to do is explore the resorts. You are coming at THE BEST time to resort hop. If you are at the Magic Kingdom, hop on the resort monorail and hop off at each of the monorail resorts; Grand Floridian, Polynesian and Contemporary. All of the Walt Disney World Resorts are completely decked out for the holidays and you can spend loads of time looking at all of the holiday displays.
Another great activity to do while it's raining is play at
DisneyQuest. We often duck in here to get out of the rain, but to also take advantage of all the games. If you're hanging around Downtown Disney, take in a movie. The
AMC movie theater has been recently transformed into a state-of-the-art theater including dining.
My favorite thing to do when it's raining is SHOP! It's the best time to do a little retail therapy and I guarantee that no matter where you get stuck in the rain, there is probably a gift shop within steps of where you are.
Cold in Florida isn't really that cold. If you forgot to pack some heavier things, you can mostly likely find them in a gift shop. During the winter months, and actually all year round, you can find adorable matching scarves, gloves and hats. You can purchase sweatshirts anywhere. Hopefully by December, you will be able to order your favorite Starbucks drinks to keep you warm.
Have a magical day!
Leslie