Whether or not the horse has a drinking problem is irrelevant to its essential nature. And even if it were touching its essential nature, such as whether it is, in fact, a horse, were questioned, the problem would not be "I don't think so", but "I do not think" in a generalized sense. And even then, it doesn't disprove existence, but rather, is incapable of affirmatively proving existence.
In short, it's not a philosophy joke. It's a joke by someone who doesn't understand philosophy, particularly Descartes' philosophy. I'm guessing whoever came up with it went to college, majored in communications, got Bs, drinks a lot of beer, watches football, and thought this would be a way to remind the rubes he drinks beer and watches football with that he did, in fact, go to college.
This amused me. It did cross my mind the joke would be better if "so" was deleted.
*MySmiley*
"Bustin' makes me feel good!"
Ghostbusters, by Ray Parker Jr.