Most State Parks allow OC/CCW. Their caveat is discharging the firearm, it is against their policy to do it, unless self-defense.
Here is the link for my reference: Department of Natural Resources
10 CSR 90-2.020 Park Management.
.....(17) Discharging Weapons. The discharging of any device which propels an object,including, but not limited to rifles, pistols, shotguns, BB guns, paintball guns, bow and
arrows, sling shots, or any devices which use burning powder, explosives, compressed
gases is prohibited, except in areas designated by the director. This does not apply to
acts of self-defense or to peace officers or park staff acting in the line of duty.
There is no reference prohibiting the carry of firearms in any of the rules I read. Some of the Park Rangers have a tendency to think it is not legal to carry in the parks; if the park ranger says you can't, request him to point it out and/or have them contact their supervisor. I encountered one at Table Rock State Park a few years ago; after a brief discussion, they followed up and understood. IIRC, they can post the buildings, but not the park.
Good luck, enjoy.....and let us know if you find to the contrary.