Redditor RohitMSasi pointed out that the opening credits of the Season 7 premiere showed the seas around the Wall had turned into ice. And yes, as you can see, the sea to the East of the Wall appears to have frozen over — possibly enough for the army of White Walkers to possibly traverse:

But Collider took it further and examined the opening credits of all previous seasons and realized that the credits have been showing winter's encroach all along.

Here are the credits to the pilot episode. Look at how the seas on both sides of the wall are deep blue. Also note the absence of any icebergs:

In the Season 2 premiere credits, not much has changed. Notice, though, how much green there is still around the coasts:

Jump ahead to Season 5 and that land mass is much whiter:

And here is the Season 7 premiere credits again, to compare. See how little blue there is in the seas on either side of the Wall: