You should check out this page,
http://www.packing.org/state/florida/, for more information.
Question you didn't ask but will be asking yourself once you are here --
"Can I carry at Disney?" - Ans. Yes w/ a permit but they do check bags and fanny packs (no metal detectors so carry ON your person and you'll be ok).
Also please, refrain from calling the theme parks you are visiting and pointing out their lack of clearly stated policies and criticizing the inadequate screening at their front gates. Disney and the large theme parks wield a lot of power in Florida and I would sure hate for them to become part of the list of places we can't go or places that might be considered a nuisance.
So carry, but carry on your person and carry very concealed and you will not have a problem. If you are made all they can do is ask you to leave, do so immediately otherwise you are trespassing, of course your family may not be so forgiving. Also keep in mind that if you ride the rides retention is critical.
Signs --
Signs have no legal bearing in florida
Posting a business in Florida has no legal bearing. If for some reason you are made OR you make it obvious that you are carrying the owner of the business can ask you to leave. If you refuse to leave then he can call the police and they will ask you to leave plus a possible criminal trespass charge. The gun is not the issue here, the issue is that you have been asked to leave, the business owner can ask you to leave for ANY reason, guns not withstanding.