Iowa code 461a.42 and iowa code 481a.7 from DNR director letter.It covers this. A person may carry on state parks, preserves, and refuges with a valid permit(i have CC permit) may carry, but cannot use that firearm. I got this link through handgunlaws.us. So basically, I can carry, but not shoot?
In most states there are restrictions on the indiscriminate discharge (not necessarily carry) of any weapon in a "public park". It varies with the state, and then again with that state may be different between parks, but most often Parks are closed to public hunting of game animals, correct? It would be my guess that any "park" that does not allow hunting, does not allow for the indiscriminate discharge of a firearm. This is more of a fish and wildlife thing than a SD carry thing, as well as public safelty.
OK, so why carry in a park if you cannot fire your weapon if needed. The answer of course is, for SD. In a SD situation, where it would be legal to shoot someone "to protect yourself, or others, from grave bodily harm" (standard type wording), you just go ahead and shoot, if you are charged a jury will not convict you of discharging your firearm. Just be very careful that you have strong grounds to fire, before you pull the trigger.
There was a case a few years ago where a gunman (now in prison) opened up with an M4 in the Tacoma Mall (also a "no discharge" area, for the same reasoning as for parks) A CPL holder shouted at the guy to quit firing and drop,,,what that CPL holder got for his efforts was he got shot up pretty badly, but that cpl holder did
not get charged because he had discharged his pistol. If you encounter a simular situation, where someone is already firing at civilians, just shoot them...do not let them know where the bullets are comming from until they are down. Might save you partial paralysis and millions in doctor bills.