The long night has arrived, you've raised an army including a dragon. Breached the wall and begin your campaign south.
Scouting the area with your dragon reports a great host stationed at Winterfell and many armies and supply trains coming from all directions towards it.
Do you spread to every town in your expansion leaving nothing alive?
Do you immediately head for Winterfell to stop any more reenforcements or supplies getting inside with what you have?
Do you march south attempting to lock out major reenforcements from the southern kingdoms?
What do you do?
My thoughts would be to drop the dragon at several small villages on all sides of the north. Quickly turn a few and leave them to spread creating disorganised anarchy across the region and fear of the unknown. Until Winterfell is undersiege you want to discourage as many living as possible from marching there by convincing them the roads are unsafe and they'd be better to hold up wherever the nearest castle is.
I would then attempt to take the Iron Isles knowing from the last long night what a pain islands can prove to be as a bastion of refuge it would be easier to strike them first without warning just a night lord and a dragon in the dead of the night start at the outside and pickup the numbers you need to take out the island or starve them in the castle.
This also offers the potential for some undead ships since they can pull a dragon out of a lake via a chain perhaps they can man some sails as well but if nothing else it removes a potential problem in the future.
As for Winterfell I think you'd be well aware that your greatest weapon is the cold. You could raid it as early as possible take out any armies outside the keep and stop anymore from getting in. Maybe attempt to kill some more dragons and then just leave it sieged and encircled but do not bother wasting manpower on it. The fortress would be overpopulated and given enough time supplies would run low and they'd turn on each other as well as the potential for disease to do some work. Leave them long enough and they will march out of desperation perhaps even fleeing north, starvation and winter will take it's toll and you can deal with that later.
At that point it would seem wise to march as far south as winter has traveled with as much of the army as can be spared and then trapping everything in the north then spreadout and backtrack to every town and village so that nothing escapes further south.
Every life taken is a new soldier raised at some point you'd have enough soldiers to hit everything at once in the south but until then you'd just clean up the north pick all the fruit so to speak and wait for winter to envelop the south. The further it spreads the greater the blitz would be during the southern assault if you spread armies everywhere at once knowing they'll hold up in their castles, you'd want to catch as many people outside as possible before they all raise alarm and abandon the villages and towns for the castles.
I'm quite interested to see what moves the Night King takes and whether any of us saw it coming or got it wrong.