I would say it depends on where you are ....
I believe State Parks now allow concealed carry throughout the parks(check with DNRC to be sure *I'm no expert*). My local state park lake is a no hunting zone, so while you can carry concealed.... I doubt a "long gun" for protection would be OK. Now an hour away at another state park you are allowed to hunt most of the lake, so during a hunting season you would be OK as long as you were in the hunting areas.... not too sure about "summer time".
Also my local ACOE lake restricts weapons in "developed areas". They do allow hunting in the "undeveloped areas"..... haven't quite figured out how you are supposed to launch the boat (developed area) to get to your hunting spot. I can tell you that guys launch and go hunt with no issues. However if you were carrying concealed while sitting at one of the picnic tables they may take issue(of course they would only find out if something went wrong). At another "developed area" they allow you to park and walk to hunting areas, HOWEVER they will chase you for bow fishing there under the "no weapons in developed areas" rule.... I guess uncased/unloaded weapons are OK as long as you don't use them right there .... And by "developed" it means a parking lot + a porta-pot.
There is also a Federal Park an hour away.... they do not allow hunting within the park, so again no "long guns". You are now allowed to carry concealed at the park with the exception of some of the buildings.
Personally I'd get the carry permit, leave the long gun at home and double check with whatever authority runs the area.
“Would it save you a lot of time if I just gave up and went mad now?” Douglas Adams