Like others have said, 1 day of rain in the forecast could easily change to cloudy in a few days. Generally, I've seen it clear out pretty well when it rains, but it depends on when it rains, and how it rains. The forecast for my Dec trip showed showers for 3 of the 4 days when I looked a week out, but I ended up in capris and a tshirt 3 of those 4 days...
If it's the morning, and a sprinkle or a quick passing shower, then everyone tries to go shopping.
If it's in the later evening, then people escape home, so enjoy it! I have a great memory of going with my BFF, and it started to rain Saturday night at like 10pm for a 12am closing... We rode Space Mountain ad nauseum until.... well, until it added nausea

And then we walked out of the parks that were relatively deserted.
Now, when I was there in December, I went into Its A Small World and it was overcast. Came out to a torrential downpour. And of course, my rain coat was in a locker on Main Street. Ugh. Worst planning moment ever! However, it was over quickly (like, 2 minutes *after* I got bundled up into my coat, of course), and it didn't affect crowds much at all.