Walt Disney World (as with all Disney properties,) prohibits the carry of "weapons of any kind".
To my understanding (I am not a lawyer, consult a lawyer, etc, etc,) Florida law is such that you must be told in person that weapons are not permitted to carry weight of law. I have seen anecdotes of people being found out by Disney Security, and being banned from the parks for life; and others of people being found out and being escorted to the parking lot to put their weapon in their car then allowed back in.
Obviously, in either case, if you are found out, are ordered to leave, and don't leave, you are trespassing, and *THAT* is a problem when armed...
Personally, I am a believer in "if they don't want me to carry, I need to decide if giving them money is worth not carrying." They say no, I either don't carry or I don't do business with them.