You just have to accept that it is normal horse communication. That's the way they rock&roll, if you please. And, believe me, the other horse definitely does not mind it, them biting and nipping at each other is just daily hierarchy setting. You can't help it. Once they set their pecking order, the biting will probably lessen over time. Besides, what looks like a serious bite to you - most likely just looks like that to you, because you're a human. They don't perceive it that way. If you interfere or separate them, you will just prolong further conflicts.
I have come a long way, to surrender my shadow to the shadow of my horse.