I thought of this while reading another question. Can the White Walkers swim?
In this scene where Bran Stark and his friends reach the Weir Tree of the Three-Eyed Raven, the wights are hiding under the ice. When I first saw that scene, I assumed the wights could swim. (Or at least that cold water doesn't hinder them.)
At the end of the battle at Hardhome, the Night's King transforms thousands of dead people into wights. If the wights can swim, why not send them out to sea to kill or capture the remaining wildling survivors? The wights could easily swarm over the rowboats and ships in the harbor. Since the king didn't send the army of the dead into the water, that would imply the wights can't swim.
We see them wade into the water to kill wildlings trying to reach the boats, but the wights never go more than knee deep.
Can wights swim? One episode implies they can, another implies they can't.
I prefer answers from the books over the TV shows. (Especially since the TV show is ambiguous on this topic.)
Edit to add: I thought of a possible solution. Is the pond in front of the weir tree so shallow that it wouldn't matter if wights could not swim? Does anybody have quotes from the books about that?