I carried a full-size tripod or monopod for 10 days in January around WDW, mostly days the tripod, and set it up all over the place, in all four parks, DD, etc, and never got any complaints from anyone, CMs or otherwise. They are most definitely allowed.
IMHO, a tripod is an absolute must if you want to take night shots.
How much of a hassle they are depends on your tripod. Mine is full-size and sturdy, so it's not tiny, but at least it's carbon fiber so it only weighs 3 lbs. A PnS camera can get by with a much smaller, lighter tripod. Other options are a tabletop tripod (set it up on a trash can or other flat surface), a Gorillapod, a Clamperpod, or even a beanbag.
If your camera doesn't have the option of a remote shutter release, you will probably also want to use the 2-second delay, so that you're not shaking the camera when you press the shutter.