I beleivr service animals yes, though i have never seen any pets in the garden or amusement park portions. The park and zoo are all open and interconnected once you enter the grounds, no checkpoints or anyone separate the portions.
Having animals at Happy Hollow they have posted a sign that clearly say pmease no animals inside. But considering the heat and the danger it brings in a quick minute, animals are at best to be kept at home safe and cooler.
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