Snakes, alligators, armadillos, black bears, all of these are just natural residents of the central Florida area (and actually pretty much all of Florida as well). Disney is surrounded by forested/swamp/river/lake areas, and the majority of resorts are bordered right up next to these areas.
As F4DisneyFan mentioned, he saw snakes at All Stars, OKW, and the Fort. You can see these animals anywhere, and chances are, half the time you do and just don't even know it. Dangerous encounters will be very rare though, so I truly would not worry about it. For instance, the bears around Disney are all tracked, and Disney keeps a close eye on them. Plus, Florida black bears aren't exactly plentiful, compared to other animals.
Now saying that, our last trip to Disney World we had a very rare, very remarkable, and potentially very frightening experience. We were at the Riverside hotel, around 9 PM and we were walking back through some of the paths that lead to the rooms. It was dark outside, but it was also a semi-lighted path, so it was pretty easy to see.
It happened so fast, that we almost didn't even believe it for a second. It crossed right in front of us from one side of the woods on one side of the path, to the woods on the other side. I had seen them in captivity before and being a nature lover (especially native Floridian species), we knew what we had seen. In fact, we both said the same thing at the exact same time.
"That was a bobcat."
That was the first time I had ever seen a Bobcat in the wild, and it reminded me of a time when I was hiking in the Everglades and cames across the rarer and more elusive Florida Panther. The Florida bobcat is a lot smaller and a lot less dangerous, but still, kind of makes you hold your breath for a second