I agree with Bill the pigmy rattlers and water mocassins concern me more than the Gators.
I will say though that recent photo of one in Florida, at someone's door was scary.
WDW is in Florida, so of course there are snakes there. Actually, snakes are much more numerous than alligators -- they are everywhere, wet or dry.
The vast majority of snakes are non-venomous, but there are at least 4 venomous species at WDW: Eastern Diamondback (largest and most dangerous venomous snake in North America), Water Moccasin (cottonmouth), Pygmy Rattlesnake, and Coral Snake. I would not be surprised to learn that there are also Canebrake Rattlesnakes and Copperheads there as well, but not sure about that.
Like most wild animals, snakes are not looking for encounters with humans, so we often walk right by them without noticing them. They are ambush hunters, so they lie motionless with some cover until something to eat comes along. When we approach, they just freeze and we don't see them, but if they are startled or harassed (in their opinion -- doesn't matter what our intentions are) they might bite. That's why Sammie's advice to keep kids from poking into or cutting through brushy areas is important.
Contrary to the old wives tales you hear, it's very difficult to tell whether a snake is venomous by appearance. There is just too much variation within species, and some non-venomous snakes look very similar. The general rule is, if you can see definitive proof that a snake is venomous you are WAY too close.
In addition, just because a snake is non-venomous doesn't mean it won't bite. Any wild animal will bite, and some non-venomous snakes (brown water snake, African rock python, reticulated python) are very aggressive biters, much more aggressive than any venomous snake.
If you see a snake, just stay a few feet away and you'll be fine.