I think it would be wise to make the distinction between "State land" and "Public land" if this discussion is to produce any real answers. Not all State land is public land......
Clay-diggins, let's just put the analogy like this, to make matters simple:
A library may be "public land", right? Or the pentagon may be on "public land", right? Yet if you go to the library at 2am when it's closed, by entering through a window, then .... you're in trouble, right ? Despite the fact that's it's public property.
Or if you go into the pentagon and waltz through officials offices looking at sensitive papers, etc... you're in trouble. Despite that it's on public property.
Thus yes, I get it. There are some forms of public land that we can't be on. Or can't be there at certain times. Or can't do certain activities on them, etc....
But all of this is via the rules and laws governing those locations. And such info can be looked up. Like in the OP's case, he first determined it was state (ok, so far so good). And now he's gone a step further and even discovered the TYPE of state (ok, so far so good). Now that he knows it's a "wildlife area", where the public is indeed not dis-allowed from being on, then ... ok. If he further worries that somehow, someway, his particular activity (metal detecting) might be disallowed, he is welcome to look up that as well. And if he found nothing that said "no metal detecting", then presto, it's not prohibited.
The rules/laws governing sites, land, etc.... is all available for the public SOMEWHERE. In other words, no law is "secret", that you can't look up, and know. It's usually available on-line somewhere. And if not, you can ask the entity in question "where can I find a complete listing of the rules-of-use regarding such & such wild-life refuge. Perhaps they'll pass you a rule's pamphlet. Perhaps they'll direct you to where it is in pdf form on-line. Perhaps they'll direct you to the binder behind the front desk. Etc.... It's got to be SOMEWHERE for public viewing. Look it up for oneself.