I'm with Stefen on this one. I'd just go. if someone has an issue, they're welcome to tell you, and no harm done. Just don't "stick out" or go in the middle of an archie convention, etc....
If you are skittish, and think you still need to know if there's some specific prohibition, just check out the website of the governing authority (there is usually a key-word search), or read the wooden sign at the entrance to the park. The reason I say to check it out on your own (if your skittish), is that, the minute you ask some authority (or someone who THINKS they are an authority), is the minute you merely allow them to say "no", simply because they said so, even though no specific rule existed (nor would anyone have probably ever given you a second thought or even noticed you to begin with.)
If it's public, and not specifically disallowed, nor an obvious monument of some sort (the white house lawn, Shiloh, Bodie, etc...) then I would consider it no different than an old school lawn.