You'll find gators all over property... Just like you'll find Armadillos, Turtles, Turkeys, Rabbits, Deer, Foxes, Snakes, and other various creatures of the wild. This is thier natural habitat.
Often times, Disney will let the gator be, as long as it poses no active threat to the guests. Once the gator grows to be a certain size, or starts to pose a threat to guest safety, the gator will be relocated. (However, 9 times out of 10... a few weeks later, another gator will appear... after all... this was thier natural habitat long before Disney came along)
As for the golf courses, yes, on occasion, you might see a gator in the water areas. I urge you, PLEASE, do not go near the gator. I've seen a lot of folks try and taunt the "baby gator"... however, I can tell you... they may look as if they can only waddle... but they can go pretty fast on the ground.