When I was on insulin I had a little blue pack that held things you put in the freezer. It came with 2 to have a spare. It was shaped so there was a groove that held 2 bottles. The pack also held all your other supplies.
I don't remember the brand, but I ordered it from an ad in the back of Diabetes Today Magazine. I am sure you could find a similar produce on the web.
It wasn't much bigger than a small camera bag and no problem to carry. WDW will supply you with a fridge for your room so you can freeze the holders.
Yes, they will let you keep your stuff at the first aid stations, but I found keeping it with me easier. Just depends on it you want to time yourself to be at the station at the right time.
The folks over on the disAbilities board would have some info on this, too.