Ok, I asked the FWC,and there answer was in Florida you cancarry a Handgun at all WMA's (not in hunting season) if you have a concealed weapons permit,as long as it remains concealed, you may do so on all WMAs except for: Camp Blanding, Raiford, Eglin AFB, Tyndall AFB, Avon Park AFB, Big Cypress and all 6 national wildlife refuges.
Hope this helps.