Check out this video that's gone viral ... 2 cops are seen patrolling Melrose Ave. in L.A. while on horseback -- when, all of a sudden, an unleashed dog runs into frame out of nowhere and begins to nip at the legs of the police horse, which still has one of the officers on it.

In response to the attack ... the other cop on the scene jumps down from his own horse ... and begins swinging his baton at the canine -- and he seems to make contact a few times.

The dog tries to dodge the hits, and it continues to go after the horse -- which begins to buck and get uneasy. Of course, the officer who's sitting up there is trying his best to steady the animal and get it under control ... but it's a tricky situation, to say the least.

Eventually, the presumed owner of the dog runs onto the scene and collects his pooch -- but he too has trouble with it ... and the officer on the ground gets one last good swing on the dog before it and its owner run off. At that point, everything settles down.

Now, we have some more info here that'll hopefully shed light and provide context -- including whether this fell onto the LAPD's radar at large, and what exactly happened in the end. Law enforcement sources tell us this incident actually happened a good year or so ago ... even though the video is just now making the rounds online.

We're told the dog and the two horses ended up being alright, and that the horses were checked on by a vet afterward. Our sources tell us the dog actually jumped out of a car window there on the street, which is why it didn't have a leash on ... so kind of a freak thing.

Our sources the civilian/owner did not get cited over this, and we're told everything sorted itself out once all the parties were able to talk. We're also told the owner wasn't mad.

That's not to say the internet isn't pissed about this ... 'cause a good chunk definitely is.

The situation has prompted mixed reactions online -- with many coming to the cop's defense, especially since L.A. has pretty clear leash laws. If you don't know, pet owners are required to keep their dogs on a leash in public at all times -- as it's prohibited for them to roam free.

Others, of course, are crucifying the cop here ... saying he completely overreacted and was harming the dog for no good reason. These are mostly the animal lovers/animal rights camps.

We had some debate about this here in our own office ... and we figured we'd present our arguments for people to digest. On the one hand, the dog was unleashed and caused a problem right then and there that could've become more dangerous.

Still ... the brutality the officer inflicts here just feels like too much for folks who can't stand to see animals suffer -- including some in our own ranks, who are passionate about this.

We suppose we'll just pose the question ... who's in the wrong here, the cop or the owner?