I used to work at the theme parks. I did security there for a few years, so I can give you an honest answer to the question you asked.
The policy for the parks is simply "No firearms, knives, chemical sprays, or any other weapons allowed on property"
First, there are no laws that would legally stop you from carrying on the property. The no firearms thing is just a policy, and nothing more. If you are on property, and you decide to carry, you 99.99% will not be caught. You don't go through any medal detectors, and the bag searches are designed to be a general deterrent for local gangs bring in guns and drugs.
Security in the parks is very tight. They may have little to no power, but the Orlando Police Department is very quick to respond to anything that happens. There are about 10 officers assigned to each park, that just walk around and wait for security to call.
However, you are on private property. You can be asked to leave for ANY reason. They can issue a criminal trespass through the Orlando Police. It doesn't go on your record, but if you get this for any reason, DON'T argue. The police there like to make arrests, because it makes them look like they have a purpose, and they get more detail hours the more calls they respond to. Accept the trespass and leave. If you do not leave immediately, they can arrest you. If you have a firearm, its a FELONY.
Its not because you have a firearm, its because you did something that made them request you to leave. As long as your not doing something you shouldn't, you'll be fine.
Long story short, you can carry, as hundreds of people do every day. Don't print too badly and you'll be fine. I recommend an ankle rig, because of many of the rides, and heat can lead to discomfort on your side. (that, and security isn't trained to look for a gun on your ankle...)
And for those that have wondered, yes, they have trespassed off duty LEO's because he said he didn't have to leave for having a firearm. YOU CAN BE ASKED TO LEAVE SIMPLY FOR HAVING A FIREARM. OR any other reason. I personally saw some one get trespassed, and the warning said "Looked at me funny." under the reason - I kid you not...