Most Park Managers are welcoming caching, particularly Earthcaches, they, as stewards of the park must be concerned w/environmental and safety issues. Here in PA one of the major reviews and at times a delay, w/the State Parks is the Endangered Flora and Fauna check. Another common requirement from other parks is staying on the trails or w/in “x” # of feet of the trail.
A permitting process, based on the awareness of the location, is becoming common w/many parks.
Just be aware of other requirements, and the development of these requirements from public parks.