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