Visitors to Florida:
Any body of fresh water in Florida has the potential for alligators.
“No swimming” means “Stay out of the water”. Period.
Most alligators mind their own business, but do not take any risks.
They also do not thermoregulate, so a non-moving alligator in the winter becomes more active in the spring and summer, especially during mating season. Mature bull alligators (males) can become territorial.
Alligators feed on smaller prey, just like any large carnivorous animal. Be especially mindful that your dog or small child does not approach bodies of fresh water.