No, that doesn't make strategic sense at all. If the White Walkers just head on south towards Kings Landing, they'll have a large force attacking them from the rear the entire way south. Not a good scenario.
However, if the Night King split his forces and put enough troops into pinning the forces in Winterfell while rest went down to King Landing . . .
But my sense is that the Night King has enough forces to swamp Winterfell. Might as well defeat the forces in Winterfell for good and increase their own forces in the process before rolling south.
Except that tht South isn't the Night Kings' main objective.. it's killing Bran and this removing the "racial memory" (if you will) before killing everybody else. He knows that he has a huge strategic advantage with the way his troops work, i.e. he doesn't have to feed him and morale is a non issue on top of being able to easily replenish his numbers for the fallen (and remember that the Winterfell crypts contain tons of dead Starks!)
So his plan is probably to raze Winterfell, kill Bran and then move on to the rest. How much damage Winterfell can do with its Dragonglass/Valyrian stell weapons and their two dragons is up for debate.
I'm guessing Winterfell will be overrun and everyone be pushed back to the Godswood where the surviving heroes manage to evacuate Bran at the last moment further South for the Big Battle 2.0 (probably episode 5) where the fate of Bran and the Night King will truly be settled as well as the looming issue with Cersei and her army.
I think their plan for the Night King is ridiculous and doomed for failure! One theme of this episode was underestimating an opponent (i.e., Cersei).
How likely is it that the Night King would fall for such an obvious trap? Not very! He'll sense Bran there and simply command thousands of troops to take him. Attempting to isolate the Night King given their situation is a fools errand. He's surrounded by hundreds of thousands of troops. We have to assume he has some intelligence.
No, I think the good guys will pay dearly for the gambit of risking a top asset. I'm guessing that Bran survives, but at great cost. The Night King will also survive, and I think the battle heads south.
It could be that Winterfell is intelligent enough to make the White Walkers priority targets and they can now be easily killed by dragon glass tipped arrows and hand weapons. Maybe Winterfell does so much damage to his troops that he is forced to take to the field and assault Bran directly (mind you, he has a Zombie Dragon so the castle walls are a non issue).
There he encounters Dany and her 2 Dragons, the Iron Born led by Theon and whoever of the heroes manages to survive the battle by that point and retreat to Bran's position.
I also firmly believe that the Night King also has a few aces up his sleeve.. chief amongst them the huge cemetary right beneath Winterfell that may be an easy troop supply for him (and explain the short trailer scene of Arya being apparently in deep trouble in the crypts).
The episode was brilliant.. i've had many frustrating discussions and comments of people throughout the years who quickly get bored with character and dialogue driven episodes and just want the action whereas i live for such well made character interactions and the machinations in between the decisive battles. If i just wanted huge fights i'd watch a Michael Bay movie (and do occasionally

Especially the fireplace scene was pure gold, seeing all these characters sitting there and knowing all their journeys and events that led them to this place is just pure awesome (the same applied to the big meeting scene last season where some characters meet for the first time ever while others meet after years again).
Points from the episode:
- Pod
Damn, son! That was some awesome singing (and now we know what he did to all those ladies back then.. he sang for them!

- Arya
Get some girl!

I wonder, if she makes it that is, what will happen if finally no one is on her list anymore.. will she be able to lay down her weapons and start to find some happiness (maybe with Gendry)?
- Future Drama
Well.. 2 huge drama points incoming and it all involves Dany and he singular, one can say manic, drive to be ruler of the seven (not six!) kingdoms. Loved the sit down with Sansa, it was a mature thing to do to adress and talk about the issue and bring it out in the open. It was good to see Sansa realing her mistake when they first met and Dany explaining herself until they hit the elephant in the room. Depending on the outcome of the batte this will remain at the core of the problem with Dany, i.e. he singular and obsessive need to be ruler. I also don't believe anymore that she does this out of the goodness of her intentions, to break the wheel as she put it several seasons back, she is now at a point where she is not that much different than most rules that came before her (maybe a bit more humanitarian than others).
This will be her second problem when she deals with Jon's revelation (i don't think the incest thing came up immediately but her reaction was due to suddenly there being a stronger claim to the throne than her's which pull out the rug from underneath her entire life).
Jon is most likely not very interested in the Iron Throne itself, if at all however (conveniently

And yeah.. when do people actually do the sensible thing?
