Well I can share a couple things with you about this since I'm in LE and have a few friends that are Park Rangers.
1) There are state parks that I have not seen any postings reference drones usage. It should be posted as far as I know.
2) Be cautious about flying near dams. If operated by US Army Core of Engineers that will be a no no in that area but not the entire Park.
3) Serpent mound was first Park I found with drone posting. And it doesn't prohibit usage of it. It tells you to ask for permission.
When we spoke with the person in charge there he had a couple rules which make sense....
Fly drone during non-peak hours in morning or evening.
Does the drone have safety precautions, obstacle avoidance, RTH. When he was advised that it was a Mavic Pro with those features he stated absolutely your welcome to fly here.
So don't take it as a negative view. They are responsible for safety of others. I think they are trying to avoid the lower end drones with no safety features at all and also want to get a sense to see if your going to be a responsible flier.
I have flown at Rocky Fork, Fallsville at waterfalls, and some areas of Ceasers Creek as well as Cowan Lake with nothing but positive experience. I also didn't fly over people but stayed in non-busy areas and all went well. Most people really enjoy seeing the capabilities of the Mavic and grew interested by saying they would like to get one.