I can't remember where I found this. Sorry, but I it answers the question, "Where did "straight from the horse's mouth" and "don't look a gift horse in the mouth" come from? Since I thought that you may have also been curious about their origins, I'm posting the answer here.
Straight from the horse's mouth: When you get information straight from the horse's mouth, it means you are supposed to be getting honest, correct information. The phrase comes from the old days when determining how old a horse was, was done by looking at his teeth. So, before betting on a horse, people wanted to check its teeth to see how old this horse was. Anyone who worked around the horse knew how old the horse was and could let the others know. Therefore, the information was acquired, 'straight from the horse's mouth' and not the owner of the horse. On the other hand, if someone gave you a horse for free, it was considered rude to look in its mouth and check to see how old it was. You were "not to look a gift horse in the mouth". Today, this means not to question the quality or motive of a gift you get from someone.