I walked about 800 blocks from home, tamed a horse, rode it back to base. I removed the saddle and walked back to get a 2nd horse. I saw the one I just ridden home, about halfway back to the place I first found them. It was still wearing the saddle, which I now had a copy of in my inventory as well. I got back on, rode it back to base to find that the first horse had disappeared. The saddle however remained duplicated. One on the teleporting horse, and one in my inventory that I had removed when I left him. The duplication did not reoccur with the subsequent horses or donkeys that I rode home, following the same path, so I can not recreate it.
A 2nd glitch I have found with horses in pre-release 1.9 v4 is that if a horse or donkey on lead runs into a lily pad that touches land, going from the water towards the land, they will walk into the lily pad rather than step onto it, get stuck, and the lead breaks. With baby animals, I had to break the lily pad to free them, then put leads back on and continue.