It looks like a dead/stuffed horse, and they probably reused the prop a few times. Each section of the cliff that the horse impacts has a lot of water there so they must have fished the prop out for retakes.
USSR 1966 (probably produced in 1964-65)...I'm sure a real horse.
You'd have to put some time in it, but it could be realistically faked. Use some real horse parts over a synthetic skeleton, and it would have authentic movement.
I figured the horse's movements that you see right when the fall starts were just the limbs catching on the cliff, because they completely stop moving after.
Edit: HOLY FUCKING SHIT IT IS A LIVING REAL HORSE! Look at its legs kicking and the horse obviously thinking "WTF!!!" at the very first millisecond you see it falling...definitely real, definitely alive, definitely fucked.