What's to stop the Night King from just sitting with his army outside the walls and wait for Winterfell to starve? The living already had limited resources and the wights don't get tired and or need food. The Dothraki's main tactic is to cause panic by either a surprising frontal assault or flanking and get infantry to retreat which doesn't really work with the undead. They needed to draw out the Night King. Using the Dragons straight away was super risky after Viserion was sniped so easily and might have been needed to kill the NK. I'm not saying no tactical mistakes were made. Putting the Artillery in front of the Infantry was lunacy and Dany should have had Drogon bite the Night King in half as soon as he was vulnerable but otherwise they were pretty low on effective tactical options.