According to Sylas, Dani doesn't even need a single soldier since it would just take 1 of her "invincible" dragons to conquer the entire planet.
not quite.
All it takes to defeat the Night King's forces is a single dragon, yes. She is actually at a disadvantage for every living troop she sends in to battle since ultimately they only add to the number of ice zombies her dragons will have to kill. It requires no special tactics or strategy. The dragons require no input or riders, this actually hinders the dragons.
Dragons working off of raw instinct fly really high, really fast and melt anything on the ground beneath them. They face a massive land based army with no ranged attacks. In addition tThe army they face are instantly destroyed by fire. These aren't World War Z or Walking dead zombies, you don't even need the fire to consume and eventually destroy the bodies. The ice magic that fuels and animates them is destroyed by contact with any source of flame whatsoever, they instantly become corpses again even if they aren't on fire. The walkers are basically made of pure ice and melt/explode on contact with dragon fire or any item imbued with dragon fire or fire magic (dragon glass, valyrian steel, etc).
The dragons alone cannot lose. only blunder on the part of man or trying to make the dragons act against their natural instinct can tip the balance out of the dragons favor.
The story so far of Dany has been one of her building up massive forces in order to conquer westeros so that she can defeat the great other and his minions with the first gift she was ever given, the dragons. The drama of the story has been about the intra-house politics and human infighting, but the tension from the story has always been can dany get there in time and not fuck it up. There really isn't any tension on who will win, it's literally no contest army of ice zombies/ice faerie creatures vs giant fire breathing dragons (The Walkers are actually closer to fae creatures in the books as described by GRRM, not so much zombie-ish things from the tv show). She was given the IWIN button from the get go, can she not fuck it up and end up losing the dragons fighting people before the great war starts and they are needed?
Now if she commits to some idiotic plan like armoring the dragons and forcing them to walk, and face the army of the dead on foot? different story.
The reality is, the easiest way to win the war for the dawn if dany does commit to some blunder, and potentially I can see this coming to pass in the books, is for someone to just kill Dany. The dragons will break free in a fit of murderous rage and just killdoze everything.