Cliche:"don't look a gift horse in the mouth"

does this cliche have anything to do with history's trojan horse or does it simply allude to the telling of a horses' age by the lenght of its' teeth?

I don't think it has anything to do with the Trojan Horse. It's my understanding that examining a horse's teeth is a way of determining its health and, consequently, its value. The phrase simply means when something is given to you (as a gift in this case) it's foolish or at least rude to question its value.