natepen, CWnut safely uses the word "usually" when saying that state land is off-limits. Because truth is, that's not always the case. There are plenty of state's lands that don't care, or just say "inquire at each kiosk you come to", and so forth. But yes, some other state say "no" from the git-go, re.: their state parks.
For purposes of Minnesota, notice that this site lists it as one of the states with an outright "no":
http://www.fmdac.org/parks/parks.htm
However, a little background is in order here: When those type lists were made up decades ago (starting with a book on subject "Treasure Laws of the United States" by R.W. "Doc" Grim) the way they went about gathering this information, was simple. They asked! Doh

And who better to ask than the state's themselves, right? So for example, Grim wrote a letter to all 50 states, xeroxed off, sent to each state capitol head legal beavers in park's dept's, asking something "what are the laws/rules regarding metal detectors in your state's parks?". And then to make his book, he merely puts all 50 reply letters in his book, and presto, you can just go travelling in your RV, and have alphabetic lists of the states, in case anyone hassles you.
Sounds simple enough, but an interesting phenomenom happened back in the '80s when that book appeared (and continues with lists like the current FMDAC one above): There were states on that list that had dire sounding wording (or outright "no's") that had never had a problem. Ie.: state parks had just been routinely detected, and no one had ever cared, or been bothered (barring obvious historic landmarks, of course). So when lists like these come out, some old-timers are left scratching their heads, thinking "since when??" You see how that works? Some desk-bound bureaucrat receives an inquiry like that, and gives the "safe answer" spinning cultural heritage stuff, disturbing wild-life, blah blah. And presto, an answer to your "pressing question". So sometimes even lists like that, you have to read between the lines.
And the states (a lot of them on that list) that just make it simple by saying "ask at each location you come to", ALSO simply became self-fulfilling prophecies: Persons would dutifully obey this mandate (afterall, you don't want to "be arrested" do you?

). And kiosk clerks, who perhaps would never have given the matter thought before, are pressed with giving authorization/approval to these odd questions. So to answer the question, they too call desk-bound bureaucrats, are probably connected to the state archaeologist, and return to the kiosk window with a "no". Mind you often time this is occuring in parks that were ...... up till then ....... detected w/o a care in the world.
It's the old "no one cares till you ask" psychology. So assuming the "reserve" you speak of is state land, sounds like your answer is "no" for Minnesota. But as to whether or not anyone really cares, or would ever notice you .......... well ......