The role of the Rohirrim at the Battle of the Pelennor fields has been vastly overstated by revisionist history from Gondor meant to highlight and strengthen the alliance between the two nations. Do not be fooled by the romanticized propaganda claiming that the Rohirrim 'saved' Gondor and that the Kingdom will forever be in the debt of the horse lords. In reality, the so called 'Final Charge' was nothing more than a minor distraction for the Orc military.
True, it did serve the purpose of redirecting resources from the invasion of the city in order to defend the Orcish flank. But the fact remains that the Rohirrim forces were far outnumbered and too lightly armored to make a significant dent in the invasion force. Additionally, the siege engines had already broken the main gates, meaning that the element of surprise came far too late.
The true turning point of the battle came with the arrival of King Elessar Telcontar at Pelargir (EDIT: please note that Pelargir is not Pelennor) leading the Dead Men of Dunharrow. Without this timely intervention, the Corsairs of Umbar would have arrived at Gondor to replenish the Orcish forces and completely destroy Gondor. Instead, Gondor received reinforcements from the South, turning the tide of battle completely and breaking the Orcish moral.
And of course, the death of the Witch King of Angmar cannot be overstated as a fact, both tactically and morally. Gondor had few defenses against the Nazgul riders, leaving them entirely vulnerable to attacks from the air. Lady Eowyn's defeat of the Witch King, leader of the invading forces, was a significant blow. Though she herself played a significant role, the same cannot be said of her brothers in arms.
In truth, the role of the Rohirrim was limited only to delaying the true battle until King Elessar Telcontar's forces arrived.
The Battle of Pelennor Fields can be divides into three main phases:
The siege of Minas Tirith
The arrival of the Rohirrim
The arrival of Aragorn and his reinforcemnts
While I won't get into the topic of who exactly the army that Aragorn brought was composed of (Some say wild men; others, Numenoreans from the south. The traditional tale is an army of the dead.), the Rohirrim's role in the battle is well-documented.
Prior to the arrival of the heavy cavalry of Rohan, think about how the armies of Mordor were arrayed. They were encamped, with fortifications set up for a siege. That is, pointing at the city. The Mordorian (while Orc is the common demonym, it really only refers to one ethnic group; Sauron's emerging empire was very multicultural) infantry was encamped and not prepared for a battle on the morning of the second phase of the battle. Combined with the preference of the Mordorians for swords and light armor, the Rohirrim ran into a perfect storm of cavalry vulnerability.
In the end, no, the Rohirrim did not win their phase of the Battle of Pelennor Fields by means of superior tactics. They exploited a vulnerability in the enemy to heavy horse, yes, but that was mostly coincidental.
You have one fine answer already. I'd like to add to it and disagree on a few points.
Certainly, the arrival of the Dead Men of Dunharrow was the ultimate deciding factor in the battle. It should be noted, however, that the arms and armor of the Dead Men were in poor condition and outdated by the standards of TA 3019. Further, the Army of the Dead suffered from uniformly poor morale and almost nonexistent unit cohesion. They generally resisted combined arms exercises with accompanying Gondor units.
However, being already dead was a key advantage: the Shadow Host took a remarkable zero casualties during the battle and its aftermath. Most scholars agree that this was the tactical "deus ex machina" that carried the day.
That said, however, I must respectfully disagree with the other expert. I'll hope to show why the Charge of the Rohirrim was much more than just a distraction.
First, the element of surprise should not be undervalued. The Dark Lord knew to expect a possible relief force, and so dispatched an army to intercept them on the Northern Road. This interception failed, when the Drúedain led the army through the secret paths of the Drúadan Forest like Ephialtes through Thermopylae. The effect of this was clear: Sauron was not expecting a relief force on the battlefield at Pelennor. This is confirmed by the archaeological record: researchers have found zero evidence of contravallation efforts while unearthing ample orcish artifice from areas adjacent to Minas Tirith.
Here, the element of surprise provided a textbook-perfect soft flank for the Rohirrim to exploit with devastating success. Orc casualty records from the Third Age are notoriously difficult to verify, but accounts from Rohan describe a one-sided slaughter in the initial stages of the charge before the counterattack and the arrival of the Witch King. If this charge had not occurred, all these forces required to counter it would have been redirected into the breached gate of the City of Kings, wreaking untold horrors.
And here I think is a good place to stop and try to answer your second question: "did the Rohirrim use superior mounted tactics against the orcs?" In my opinion, they did not. These were fairly standard cavalry tactics, executed to near perfection. They arrived quickly, unexpected, and with good spirits to a battlefield where they charged an unprepared flank of individually inferior infantry on an open, flat plain. This is the best-case scenario, but it would seem that even this was not enough to change the battle's outcome. When Elessar Telcontar and his army arrived in Pelargir, the counterattacking force of Mordor's Eastern allies had begun to turn the tide. The Oliphaunts wrecked their shit, the surprise had worn off, and Sauron's army had made their counterattack with overwhelming numerical superiority, including reinforcements from nearby Osgiliath.
The first part of your question is also worth answering now, and here's where I'd disagree with those who would downplay the importance of Rohan's entry in the battle. The consequences were strategic and critical.
In all such ancient magical warfare, a good healthy chunk of the death comes after the battle has been decided, and Pelennor was no different. The fleeing orc armies were mercilessly pursued by the remnants of the Rohirrim, severely reducing the orcpower available to Sauron for later engagements. And here, their cavalry performed a duty that could not be accomplished by the Men of the Mountains, who were on foot. Plus, the Oathbreakers' terms of enlistment were sketchy in the first place and no one was entirely sure who could tell them to do what once the battle concluded. They were great tactically but as a whole had some serious strategic flaws.
But the reduction in Sauron's orcpower would prove to be decisive in the war. When the Army of the West made their final desperate stand at Morannon, they did not hope to achieve a victory on that battlefield. Instead, the goal was to distract the Lord of Barad-dûr and trick him into pouring all his armies through the Black Gate to meet them. Consider, then, the scenario where a significant portion of his invasion force survived. Perhaps he could have sent them instead. Or if they weren't enough alone, perhaps he sends 50% of the Army of Shadow.
Do Sam and Frodo make it through to the Crack of Doom if this is the case?
We can't say.
But to say that the role of the Rohirrim is vastly overrated? I think not.
Edit: changed 'manpower' to 'orcpower' - hope no one was offended
I believe that the Biopic "Lord of the Rings: Return of the King" may have misrepresented the effectiveness of Rohirrim cavalry in turning the tide of the battle.
The initial charge to the rear of the Mordor forces most certainly would have had a devastating effect on not just the strength of the Orc army but also the morale of the Orc army. However given the size of the Mordor forces, they would have quickly been able to reposition and turn to face the Rohirrim.
Once this occurs, if the Rohirrim forces were indeed all mounted on that fateful day, the battle would have ended differently. In a stand up fight between standing infantry and standing cavalry, infantry tend to win. Especially against the lightly armoured cavalry the Rohirrim favoured. The Rohirrim forces would not be able to adequately disengage and reform for a second charge without facing brutal losses, losses that surely would have broken the fighting ability of the Rohirrim forces.
What I believe occurred was a brutal initial charge from the Rohirrim that plunged deep into Mordor lines, and the salient created in Orcish lines was filled with Rohrrim infantry. The edges of this salient were prevented from closing with harassing actions from the Rohirrim cavalry, which would have withdrawn from the front lines once the Rohirrim infantry caught up.
Another possibility is that assuming the majority of the army was mounted, many forces dismounted and fought as infantry, with the royal guard acting as heavy shock cavalry units harassing the flanks of the orcish forces.
I hope this clears up some of the inconsistencies surrounding the Biopic. It's understandable that they presented the Battle of the Pelennor Fields in the manner they did, as a massed cavalry charge has much more romance around it than the truth.
I feel like /askhistorians subreddit is being april fooled. I just realized half of the posts that made it on front page don't make no sense to me. And I'm at [8].