The phrase (straight) from the horse’s mouth refers to information and means from the person directly concerned or another authoritative source.
This phrase is from horse racing, and alludes to the presumed ideal source for a racing tip. The earliest instance that I have found is from Bell’s Life in London and Sporting Chronicle of Sunday 22nd September 1861:
CESAREWITCH:—Rank Outsider. A raker to win, straight from the horse’s mouth and two steamers for places. Cambridgeshire: a dead heat. Do not delay. Send me an addressed envelope, and eight postage stamps towards expenses. Direct Silas Merrifield, stud groom. Mrs Darcy’s, 43, Cleveland-street, Warren-street, London, W.
The earliest figurative use that I could find is from the column This Busy World in The Manchester Weekly Times of Friday 20th July 1900:
“Summer has come at last, and in full force.” Thus a sapient contemporary. So nice to be kept well informed, don’t you know! If one hadn’t the nimble copper to buy one’s morning paper, one might have been left in dense ignorance of the fact. I’d a bit of a notion of an idea of a suspicion that the caloric in the atmosphere was constructed so as in many ways not to resemble the depths of winter, but it’s nice to be furnished with correct information straight from the horse’s mouth, so to speak. Otherwise one might fall into the error of donning one’s winter great-coat and over-shoes, and wrapping a shawl round one’s shoulders. But you buy your paper, and, on learning that “summer has come at last,” you dig up last year’s straw hat and drink things with ice in. Useful things, newspapers.
It is sometimes said the phrase originally alluded to examining a horse’s teeth to establish its age and therefore value. A horse’s teeth reveal its age, just as old people without dental care suffer from receding gums and become long in the tooth. By examining a horse’s teeth, an expert can make a good estimation of its age.
But this explanation only applies to horse buying. In horse racing, the punters already know the horses’ ages, and it is difficult to imagine some extremely suspicious punters going to the stables and examining the horses’ teeth in order to ascertain their ages…