This is the Wallsburg Group Area in Deer Creek State Park, right? (Had to Google it).It appears that Walsburg Bay Group use area has a sign posted stating "No Firearms and Hunting"
I checked, it appears that this is a state park.
My understanding is that they cannot regulate carry.
Is this correct?
If so, then you're absolutely right. They may not restrict lawful carry of firearms. They can restrict hunting, of course.