We know that parks are specifically excluded as prohibited places in Oklahoma's Self Defense Act. I don't know whether any specific state park is on leased land belonging to the Corps of Engineers, and I'm not sure whether that would even make a difference as to the legality of prohibiting lawful carry.
I attempted to call Kris Merrick, the Director of Parks with Oklahoma Department of Tourism. She is on vacation. I talked to her assistant, and he told me they are aware of the state law, but he wasn't aware that there were still signs posted. He took my contact information and promised to get back to me.
You need to be talking to the chief ranger, any of the ranger stations at any of the parks can get you his name and number. I spoke with him about a year ago about Thunderbird being posted. The rangers are aware that someone with an SDA can carry in the park. The "No Firearms" signs at state parks are for those persons who are not licensed. The big crowd of these folks are the party crowd...the ones that like to bring the liquor store to the lake with them.
At the time I spoke with him, he told me you had to be careful of land that was inside park boundaries but belonged to the Department of Wildlife. Since different money paid to maintain the land, it fell under different rules. The same would probably apply to CoE land/projects. Only that portion of the land that belonged to CoE would be regulated.
Just for fun I contacted CoE to ask about how this works at state parks...unfortunately the person I spoke with at CoE was clueless and since I used Lake Arcadia as an example, they directed me to call Lake Arcadia, so I attempted to call the number they gave me and got a fax number. I called the lake and after arguing the state law with a seasonal worker, I was put on hold and then she came back and said she spoke with a supervisor and I was told that all of Lake Arcadia Park is on federal land.
I also called Beavers Bend State Park and was transferred to a fellow by the name of Jim. Jim told me that they lease the land from CoE so they are considered a state park and carry is allowed at their particular park.
I guess the bottom line is if the park is on any kind of CoE property, call the park and find out first.