The Winged beasts vs The Eagles

[Legate of Amon Lanc]

What you say here, Boro and Raynor, is true, but still I don't think the Eagles would have to come to Gondor just because some battle is fought there. Don't let us forget - as Gandalf says - that different battles of almost or the same importance were fought at that time also in the North, and we don't know whether the Eagles joined them or not, but if they were to join any of the battles, then I think more likely in one that took place near to them. In the light of this it's only logical that they arrived at the battle of Morannon, when the main battles were already won on the North. And still, note that according to the Tale of the Years, the battles of Lórien (the second one) and Dale were fought several days before and still the Eagles arrived at Morannon only in the last hour (the Nazgul were just driven off, but 99% of the battle they were flying above the hosts undisturbed). So what you said about Gwaihir hearing news about the trouble in Gondor, Mansun, I think would make no difference - he had the same sort of enemies nearer to his own nest, and he could not be sure whether there are going to be any winged Nazgul at Minas Tirith or if there are not going to be any here on the North until the battles started (if he even knew about their existence, which is not definitely sure).

As a side note - please don't let ourselves get influenced by the movie nonsense (and I presume you are not, I'm saying that just to be sure) - Gandalf had nothing to do with the Eagles coming to Morannon, they arrived on their own account. I would presume them to be "driven by fate", them being birds of Manwë and all, but it is also possible that they simply decided that the North is more or less safe now and that they'll try to help in the final battle (of which, again, they could have learned by some "divine message" or how to call it). (Is not something about the reason of their coming in the Letters, for example?)

And if I were to be indeed nasty to the Eagles, then what exactly is said about the Eagles and the Nazgul is just this:

Originally Posted by Cormallen Field

There came Gwaihir the Windlord, and (...)[other eagles]. Straight down upon the Nazgûl they bore, stooping suddenly out of the high airs, and the rush of their wide wings as they passed over was like a gale.
But the Nazgûl turned and fled, and vanished into Mordor's shadows, hearing a sudden terrible call out of the Dark Tower...

So technically, the Eagles arrived only to pick up Frodo and Sam. "Group Alpha, to the evac point!" The Nazgul, as we see from the quote, did not turn back because of the Eagles, but because they were called back by Sauron (to stop Frodo), that is clear. It just happened that the Eagles arrived at the same moment (and who knows, maybe if the Nazgul had time to fight back, the Eagles would tear the winged beasts to pieces). But all the time the Morannon hosts fought under the shadow of terror, and the coming of Eagles was just one of (though important) the factors to boost the morale of the western armies in the end.