Why would Hades visit a battlefield?
Hades, apparently, was present in the battlefield when Hercules besieged Pylos:
And so suffered monstrous Hades even as the rest a bitter arrow, when this same man, the son of Zeus that beareth the aegis, smote him in Pylos amid the dead, and gave him over to pains. But he went to the house of Zeus and to high Olympus with grief at heart, pierced through with pains;
Source: Hom. Il. 5.395
This is one of the rare instances we see Hades outside the Underworld. One interpretation for his presence in the battlefield is that he was there collecting or overseeing the collection of souls ("amid the dead"). This interpretation, however, feels to me like an attempt to attach Christian symbolism to the story.
Are there any other references for Hades visiting battlefields? And if so, are there any explicit mentions on what exactly was the reason for him being there?
Before reading this question, I was of the impression that Hades only left the Underworld once to visit Olympus, I can't remember why though... I don't think he really visited battlefields in the same way a Valkyrie would have. Would be interesting if he did though.
Indeed, the city of Pylos, in Elis, was one of the few places with a cult of worship dedicated to Hades. This his probably why he cared enough about the city to be personally present for the battle. There was one cult in the main city itself:
 The sacred enclosure of Hades and its temple (for the Eleans have these among their possessions) are opened once every year, but not even on this occasion is anybody permitted to enter except the priest. The following is the reason why the Eleans worship Hades; they are the only men we know of so to do. It is said that, when Heracles was leading an expedition against Pylus in Elis, Athena was one of his allies. Now among those who came to fight on the side of the Pylians was Hades, who was the foe of Heracles but was worshipped at Pylus.
 Homer is quoted in support of the story, who says in the Iliad: “And among them huge Hades suffered a wound from a swift arrow, When the same man, the son of aegis-bearing Zeus, Hit him in Pylus among the dead, and gave him over to pains.” Hom. Il. 5.395-397
If in the expedition of Agamemnon and Menelaus against Troy Poseidon was according to Homer an ally of the Greeks, it cannot be unnatural for the same poet to hold that Hades helped the Pylians. At any rate it was in the belief that the god was their friend but the enemy of Heracles that the Eleans made the sanctuary for him. The reason why they are wont to open it only once each year is, I suppose, because men too go down only once to Hades.
There was also a nearby precinct devoted to Hades at Mount Minthe, a mountain named after a nymph who was Hades' concubine:
Near Pylus, towards the east, is a mountain named after Minthe, who, according to myth, became the concubine of Hades, was trampled under foot by Core, and was transformed into garden-mint, the plant which some call Hedyosmos. Furthermore, near the mountain is a precinct sacred to Hades, which is revered by the Macistians too, and also a grove sacred to Demeter, which is situated above the Pylian plain. This plain is fertile; it borders on the sea and stretches along the whole distance between Samicum and the River Neda. But the shore of the sea is narrow and sandy, so that one could not refuse to believe that Pylus got its epithet "emathöeis" therefrom.
Source Strabo, Geography 8. 3. 14