1) "Preserve" is in the name of the facility, as does Rockefeller.
2) Cranberry users have to "stay on designated hiking trails" (https://parks.westchestergov.com/cranberry-lake). There are signs to that effect in Rockefeller too.
3) Cranberry's web page specifically says it is "Cranberry Lake Preserve is a designated Biodiversity Reserve Area."

Therefore, these are preserves, not parks.