When I went, Waterworld played in a light rain but I believe later shows were canceled when it started to downpour. If the rain is heavy enough they give out hot chocolate and coffee and lines are usually a little shorter than usual so I would definitely recommend going if you don't mind the rain.
The rain day guarantee ticket has been eliminated because most of the outdoor venues which would cancel during the rain no longer exist. Waterworld and Animal Actors do cancel during inclement weather situations. I believe Dino Play, stilt walkers, and the water area of SSFL closes as well.
I will be interested to see if Hippogriff will be added to this short list.