Well here’s an interesting take on the battle by a military strategist.
https://slate.com/culture/2019/04/battle-winterfell-military-analysis-tactics.html
Cavalry
Team Alive’s use of cavalry has received harsh criticism from analysts, in part because of
the near-complete annihilation of the force within minutes of the beginning of the battle. Team Alive deserves some of this criticism, but the cavalry attack is best thought of as a low-odds gamble in a difficult situation than as an error in judgment.
The success of a cavalry attack against infantry requires either flanking (hitting a formation on its side while some other group “fixes” its front) or a shocking frontal assault that disrupts the formation. Both of these depend more on psychological than on physical factors. Fear of being attacked from two sides induces infantry to break and flee, just as fear of being overrun causes infantry to throw down their weapons and run. In either case, cavalry runs free and kills until the infantry can pull itself back together. But crucially, success depends on the ability of the cavalry to induce panic.
We also know from ancient and medieval sources that commanders struggled to keep even experienced cavalry under control. Once cavalry left sight range and hearing distance of a commander, it was effectively on its own and not manageable. Cavalry formations commonly abandoned the battlefield to pursue objectives distinct from those of their commanding officers. Even as recently at the Battle of Gettysburg, Gen. Robert E. Lee lost contact with his cavalry, leaving him blind in the fight against the Army of the Potomac.
Team Alive knew enough about Team Dead to guess that the Dothraki faced a kind of infantry that they had never encountered before; one without fear and thus invulnerable to shock and flanking. Moreover, in the dark, the Dothraki probably could not even identify the enemy flank. Although it’s not clear that Team Alive had a well-thought out plan for the cavalry charge, it may have believed that it could take advantage of the lack of discipline of Team Dead (which did not fight in tight phalanxes or with standardized weapons) in order to reach and attack the “middle management” of White Walkers. Alexander the Great employed a variant of this strategy at the Battle of Gaugamela.
While all of this makes theoretical sense, it also runs counter to decades of Dothraki fighting experience. When Dothraki fought undisciplined infantry, that infantry broke and ran. When Dothraki fought disciplined infantry (the Unsullied, for example), the infantry took casualties but could retreat and maintain integrity and mobility. At the Battle of Winterfell, Team Dead’s infantry simply absorbed the greater part of the Dothraki cavalry without breaking and running. This left the cavalry immobile and largely defenseless against attacks from every side. The Dothraki likely did not envision their attack as a suicide charge, but they had limited tools with which to judge the effectiveness of Team Dead.
None of this makes the cavalry charge a good idea. But the mistake was made in the days before the Battle of Winterfell, not in the minutes before the charge. The best employment of the Dothraki would have come as long range scouts and skirmishers in the days before the battle. Even then, however, their utility was limited; cavalry often succeeds by disrupting supply lines and ambushing foraging parties, and Team Dead needed neither of these. And in any case, unless Team Alive spared a dragon for air support, any accumulation of Dothraki would have been vulnerable to Viserion. If the Dothraki had not charged, they would have found themselves pinned against the infantry, their mobility lost. If they had moved right or left in search of Team Dead’s flanks, they would have run the risk of being flanked themselves (Team Dead also had cavalry, and its infantry was fast and fearless) or destroyed by Viserion and the Night King.
At any rate it’s an interesting read on battle.
(Also Arya falls under Team Alive - Special Forces )