Well, I am not at Disney right now, but I can tell you from my over-packing bad experience that 3 sweatshirts would probably be just fine. I suggest wearing t-shirts under them so they don't get as dirty.
I believe that the weather in Orlando right now is very warm (upper 70s). I am in Atlanta and we have been wearing short sleeves and capris with a light sweatshirt/jacket and it has been fine.
Do you have any zip up hoodie sweatshirts? This is what my family uses. They are so easy to tie around your waist.