Rum Island Springs is a county park. Not a state park. I just went to their website, and tried variations in their word search box of "metal" or "detector" or "detecting", etc.... I see no prohibitions. And then I tested the word search function just to make sure it's not lame. By typing in "dog" and "leash", for example, and ... yes ... rules regarding dogs and leash come up. Hence yes, the search function searches adequately . Thus if it's silent on the subject, then presto, it's not prohibited.
And you say "... and others". It would depend on city, county, state, federal, or private. So you'd need to specify which "spring" you are referring to. But in each case, all you need to do is look up said rules for yourself (rather than asking a bored pencil pusher and risking a "safe" answer). Personally, I think even that is over-thinking it. I just hit any park I come to, unless 1) I see a sign to the contrary, or 2) it's an obvious historic monument with bored archies standing about.
As for the state park part of your question: From all that I've read from FL folk, the inland land (terra firma) parks are a no-go. But the state park beaches are fair game.
Of course avoid obvious historic sensitive monuments. But beyond that, don't over think it. It is very rare for any county or city to have ever dreamt up a rule specifically addressing md'ing. You don't need an "express allowance" (eg.: a law saying "metal detecting allowed here"). Silent on the subject is adequate. Of course, for nice manicured turf, be aware that a man with a detector might have ... uh ... "connotations" (that you might be about to leave a hole). So pick low traffic times so as not to be a nuisance or attract gripers.
