Game of Thrones: Why Don't the White Walkers Go Around the Wall?

In the Game of Thrones season premiere, the Hound (Rory McCann) had a vision that the Night King and his army are heading towards where the Wall meets the sea, leading some fans to wonder: why don't they just go around the Wall?

Given how close we are to the end of Game of Thrones, it's pretty safe to assume that at some point in the final two seasons, the White Walkers will make it into Westeros.

This theory not only covers the idea of the Night King's army swimming across, but also why they don't use their magical winter abilities to freeze the water and walk across.

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Because of this alleged natural aversion to salt, the White Walkers might not be able to spend long periods of time in salt water, which would make swimming or walking across sea near-to-impossible for them.

There are mountains on the west coast once you cross south of the Wall and a fairly organized batch of soldiers at Castle Black towards the middle, so Eastwatch could be seen as the easiest access point through the Wall and into Westeros.

[...] when you have a character like Jim Broadbent's archmaester definitively state that the Wall has always stood and always will stand, you know that the Wall is definitely going to fall.