The opening credits of a Season 7 episode also hinted that the winter might be cold enough to freeze the waters beside the Wall; if enough water freezes hard enough, the army could simply walk across the ice and around the Wall.
Then, there’s the reality that the only thing that stands between the army of the dead and the folks of the Seven Kingdoms is the undermanned Wall.
That said, the odds are pretty good that the Wall is coming down at some point, and not just because Jon left Dolorous Edd in charge.
Even with Tormund and his wildlings manning some of the neglected castles of the Night’s Watch, there’s an awful lot of ground to cover, and the magic that has protected the Wall for generations might not be entirely intact anymore since Bran — touched by the Night King in Season 6 — passed through the tunnels.