Open carry in FL State/national Parks ?

I just read about the Law allowing carry in National Parks and it seems that the law is specifically speaking about concealed carry for CCW holders. This is not a Concealed Carry Question but seems like a good place to ask.

From what I read on the FL State laws on "lawful use" I (as an Army Reservist) would be legal to Open carry a Pistol or Rifle say if I wanted to do some serious rucking and Land Nav practice in a National or even State Park correct?

(3) LAWFUL USES.--The provisions of ss. 790.053 and 790.06 do not apply in the following instances, and, despite such sections, it is lawful for the following persons to own, possess, and lawfully use firearms and other weapons, ammunition, and supplies for lawful purposes:

(a) Members of the Militia, National Guard, Florida State Defense Force, Army, Navy, Air Force, Marine Corps, Coast Guard, organized reserves, and other armed forces of the state and of the United States, when on duty, when training or preparing themselves for military duty, or while subject to recall or mobilization;