NOT ANIMAL KINGDOM!!!
They do not allow straws into Animal Kingdom and I have heard of them taking the juice box straws as well. It is a hazard for the animals. You can bring the juice boxes in and then squeeze them into a sippy cup or similar.
That being said. We went to the local zoo here today(no restrictions on straws being brought in, but they dont have them at the zoo) and I froze the juice boxes, water bottles and grapes we took for about 2 hours and they were sooo good and cool when we got them out in the 90 degree heat.