So it's an interestingly named park, the city parks and rec website calls it a park but the park's name is a preserve. https://www.copperascovetx.gov/parks/
And one article from the local news exclusively calls it a park but mentions the community desire to preserve it. https://kdhnews.com/news/communities/as-ogletree-gap-undergoes-gradual-change-the-park-continues-to-represent-the-longstanding-beauty-of/article_528e8dcd-e55b-5375-830c-86a08113d866.html
So I'm not sure if this is actually a preserve with any added protections.