Personally, I would not recommend taking a standard tripod into the parks. For starters they are bulky, you don't want to carry them all day, and even stowing them in a locker means having to carry the tripod to and from when you're ready to use them. Another problem is it's easy to be a "hazard" with a full size tripod. I don't think Disney has a stated policy, but many parks do not allow tripods to be used due to the fact that they can be tripping hazards. Other places (not WDW) may require you obtain a "tripod permit" before using one (NYC is a good example). At busier times I could see a CM asking you to please not use a tripod.
However, an even better reason for not using a tripod is
you don't really need them. Fence railings, trash cans, stroller handle bars, lampposts all offer enough stabilization to allow excellent night-time shooting. If you want to change the angle of the camera, use a bean bag to get the right angle while resting the camera on a fence. Here are some examples. Some have exposures of over 10 seconds. All of them were handheld using the objects mentioned above to steady the camera. All of them were taken on auto-exposure (Aperature Priority) ISO 200, f5.6:
Illuminations 4 Seconds
Illuminations 10 Seconds!
Illuminations 1.6 Seconds
Illuminations 2 Seconds
Illuminations 1.6 Seconds
Kids playing with twinkling walkway lights at Epcot, used a lamppost, 2 seconds
Light Chasers
Spaceship Earth, using the handle bars on a stroller: 1.6 sec
Epcot 1.6 Sec
Wishes from the wooden walkway across from TSI, used the walkway railing:
Wishes 6 Seconds
Wishes 6 Seconds
Wishes, on "foggy" Christmas Day 2004, using a lammpost:
Wishes 1/2 Second
. 
