At the end of the Massacre at Hardhome in the 5th season of Game of Thrones, the army of the dead stood on the shores watching as Jon Snow and the survivors very slowly rowed away. From a narrative standpoint, it’s easy to see why the show needed the ice zombies to stop here, as it delivered one of the show’s most impressive and terrifying moments — the raising of the dead with a hand gesture by The Night’s King. But it also raises some fundamental questions about this undead army. Are they afraid of water?
What makes you believe they stop out of fear?
or to put it another way; why would the White Walkers/Undead try and swim through the water? what would they possibly hope to achieve?
Any effective assault against a boat by an attack force that is in the water, swimming, is pretty implausible. The strongest swimmer would struggle to catch even a leisurely paced boat, and the army is without projectiles. There would have been no point in the White Walkers 'swimming after' the boats.
One thing that should be mentioned: if white walkers/whigts can easily swim or even perhaps build boats in time, then what's the point of THE WALL in the first place? It is unlikely that first man & children & giants pulled such enormous physical and magical effort, without occurring to anyone that undead can swim or build boats.
More likely wall was built with advises from children. Perhaps magic that allows White Walkers life (or whatever that is called in their case) is either dispelled under lot of water, or they are to heavy to swim due to no air in lungs. In this case they would be able to walk on sea bottom if water pressure is not too much. I think at the end of battle we see some weigths touching the water, so it's surely not fatal for them, although we don't see Walker in water.
I support the fact that swimming against the ships will be no use even if 100k of weights attacked together. Furthermore, why would Walkers be hasty to catch them while running? Living can't hide anyway, it's just a matter of time for the dead. Plus any survivor seeing such scene of tens of thousands simply rising with light blue eyes is surely more devastating for the living south of the wall when they hear about what happened, than catching few more survivors. Walkers are not mindless zombies, quite opposite as we know, and won't perfomr rushing or foolish attack because of hate or bloodlust. We see Night King actually savoring the moment of showing horror and supremacy, and since he is self-conscious and intelligent, that might not be just his ego at work but also attempt at psychological warfare. Like "You think you killed a Walker with Valyrian steel so you have something on me? Look what I have".
So not pursuing ships and boats might have multiple reasons. They surely don't fear the water, even if it is harmful they simple know to avoid it. But this question was on my mind more than once. Why would it be mandatory for walkers to break the wall? It is harder for them to attack south of the Wall by swimming and then landing on shore, but there is too many of them, they can attack by night, simply makes no sense that Wall would be built if they can swim or mind-control the weights into boat building. That would be a huge hole for Martin. Hmmmm..... unless undead need allies too >:D That would be a schock :D
There is not clear indication that they are afraid of water. However, it may be possible as we know very less about that.
It seems to me that they simply because White Walker and their army of Wight had no chance of swimming and reaching the boats. Lets assume they swim and reach near boat, then also as soon as they try to ride on boat, Jon snow and wildlings will kill them. Simply see the possibility of them trying to climb on boat ,swimming at same time while wildlings already on boat hitting them with swords and axes.
One more thing to consider, white walkers are very less in count (2-3) , they mostly rely on Wights for this task. Who may or may not know how to swim.
On similar note, we see the gaint swimming in water, it means its having depth like sea or something, there is lot chance that Wight will get drowned in water.