I don't know of a particular story but I would expect it comes from the fact that horses do not often get themselves into situations that they cannot get out of or that are dangerous.

By the way, it's common sense, not the common sense.

I like Susanne's answer. Here is another explanation, how factual it is, I don't know. But it does reference some sources. I don't think that we ever think about the origin, we just know what it means ;) http://www.phrases.org.uk/meanings/horse-sense.html