If you do not have the beverage in a glass container (must be in plastic), you can carry it all around the three parks that serve alcohol. You cannot carry it out of the park, nor can you carry alcohol into a park.
I would add that while carrying drinks around the parks is ok (except MK) other than WS, it's not the most casual, relaxing experience with throngs of people, kids bumping into you, etc. I prefer to sit in one spot and relax with a beverage. YMMV.
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