This happens to me consistently, but only after traveling long distances on the horse (roughly 1,000 blocks.) MC v1.10, Java runtime 1.8.0_66-b18, Windows 10 x64, no Optifine, pure vanilla. I can hear the entity's sound effects as well. Relogging corrects the bug.
Still present in 1.10. Is this ever going to get resolved? It's over 3 years old now...