ETA: Make sure you invest in a stroller cover and always put it on when entering an attraction if the skies look iffy...
In October 2011, we had two straight days of rain, and we just got our ponchos on and off we went! We still had lots of fun, especially in Epcot where it was nearly deserted. Well, deserted for Disney anyway.
And I agree about not trusting the Florida forecasts-they called for rain for a third day while we were there and it was hot and sunny all day.