The lawyer answer is it depends. The boiled down simple issue is what notice was provided to the person reading the sign? Signs are meant to inform you or direct you to take a specific action so that you can make an informed, appropriate decision about your future conduct (speed limits, handicapped parking, no diving too shall, etc.). You can make a common sense argument that "no swimming" does not adequately warn of the danger that was present. I.E. do not swim could mean no lifeguard, it could mean boats or jetskis are in the area so you cannot swim, it could mean pollution, it could mean electrical wires present, or it could mean dangerous predator lurking about. Disney is in the best position to provide the reader/guest with the information necessary so that the reader can make an informed decision about the conditions of the lake. They already do this by having height restrictions on their rides. Those restrictions essentially tell the consumer that Disney knows from its own engineering tests/inspection that it is not safe for you to get on this ride if you are under 3 feet tall, therefore Disney will not let you on it.
So, does a "no swimming" sign really give notice to the individual that if you go in the water you could get killed by an alligator? No. And I would think that is a very specific thing that most people would want notice about (like the height requirements on the rides) considering this appears to be private property that is controlled by a corporation that is charged with a higher duty of care to insure guest safety as they are providing lodging/innkeeper services.
And that's the second and probably biggest issue: if you can show that Disney knew or should have known that alligators were present in the pond and the best warning you gave guests was "don't swim," that's weak, lazy, and not very safe. Why? Because I can see the giant hole ahead of where I am walking, I can see that a gallon of soda has been spilled on the grocery isle I am about to walk down, I know sharks live in the ocean and I am currently swimming in the ocean, I can see the sun shining and starting to burn my bare skin so I better put on sun screen, and I can see that this pool has no water so I probably should not dive in. No one is going to see an alligator swimming in a murky lake that was made by and apparently controlled by a resort/entertainment complex who chose to put a makeshift beach on it that would draw people closer to it. Therefore you need to warn me if you know or had reason to know that an alligator was or could be in there.
Now if you want to get more intricate, you can do a Florida statutes and case law search to determine what the regulations are about warnings for alligators in bodies of water. This will likely bring up some elements of "control" in regard to who owned the lake and what duties a private individual has with regard to riparian (water) rights in these circumstances, compounded by the higher duty of providing lodging/innkeeper services and creating an attractive nuisance type atmosphere with the beach setting. I find it hard to believe that the city, county, or state has any ownership, control, or duties over this lake, but you never know. As I pointed out yesterday in my post, the best way to litigate this case from the plaintiff's perspective is with the recently adopted
Reptile Theory. Many posters on this board have already bought this train of thought (I confess I am probably one of them). The defense will have their own arguments and perhaps they will get saved by some statute that discharges their duties by merely posting a do not swim sign. But if they knew or had reason to know there were alligators in the lake and the best you could come up with was "don't swim," that's a hard sell to 6 jurors (Florida uses 6 in civil court, not 12 like many other states).