I know the wildlife management areas I go to specifically state "All firearms shall be securely encased and in a vehicle, vessel, camper or tent, during periods when they are not a legal method of take. Persons in possession of a valid Concealed Weapon or Firearm License may carry concealed handguns."
As of February 22, 2010 carry in National Parks and Preserves is allowed if you have a CCW valid in that state.
"As of February 22, 2010, a new federal law allows people who can legally possess firearms under applicable federal, state, and local laws, to legally possess firearms in this park. It is the responsibility of visitors to understand and comply with all applicable state, local, and federal firearms laws before entering this park. As a starting point, please visit the federal Alcohol, Tobacco and Firearms website and select the state that you are interested in from the list on the right side of the page. More specific information about state permit regulations can be obtained on the following websites:
Florida:
http://www.nps.gov/bicy/parkmgmt/firearms-regulations.htm
Federal law also prohibits firearms in certain facilities in this park; those places are marked with signs at all public entrances."
You know the way its worded I would think that you could open carry while hunting, camping, or fishing.