Just checked the weather forecast. During the time you're there, it will be very warm and humid during the day (upper 80s with a lot of humidity), possible afternoon showers most days, and cooler evenings (low 70s).
I'd say be prepared for the rain - ponchos come in very handy. (I use the "disposable" ones you can buy at Target for 89 cents - you can just throw them away when you're done, and you don't have to try to fold down the big WDW Mickey ponchos into a backpack to carry around.) It usually only rains for a little while in the afternoons. Or you might be able to get away with umbrellas for everyone, as long as it isn't raining too hard.
I usually go the first week of October (am leaving in 2 weeks!) and like to carry a light, long-sleeve layer to wear in the air-conditioned buildings. If it's really hot and humid, the air conditioning can be very refreshing at first, but you can get chilled pretty easily hopping back and forth between inside/outside. My rather unusual solution on my last trip was a long-sleeve denim shirt. It's lighter-weight than a sweatshirt and folds down into a backpack or messenger bag pretty easily. For me, it was better than a bulky sweatshirt, and I could roll up the sleeves if I needed to.
Check the weather forecast right before you go to see what the chances of rain will be. That'll help you pack!