The rules don't specifically mention painting. As long as you find a spot where you aren't blocking the path for the other guests, I doubt anyone will mind.
If you set up to paint outside of walking paths... on a bench spot or one of the observation spots, and leave no trace you should be fine. I've done it before.
I don't think there's any rules against it. They don't allow runners or people biking on the trails, so there are some rules regarding the use of the area - probably more about not getting in the way of other people. There's not a lot of places to sit, though there are some benches spread around the walking trails.
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