The great Irish poet William Butler Yeats died on January 28th, 1939 in the middle of winter. That's what Auden is referring to when he says that Yeats "disappeared in the dead of winter."
He goes on to say that "The day of his death was a dark cold day." Auden is speaking both literally and metaphorically here. January 28th, 1939 was cold and dark because it was in the middle of winter. But it was cold and dark in the metaphorical sense in that the world had just been robbed of one of its greatest poets.
On this cold winter's day, the mercury has sunk "in the mouth of the dying day," the brooks are frozen, snow disfigures public statues, and the airports are almost deserted. Although this is all due to the season of the year, it seems as if it's somehow connected to the death of Yeats, as if the wintry world is in mourning for the death of a great poet.
The earth may be frozen in the dead of winter, and Yeats the man may be dead. But Yeats the poet lives on, "scattered among a hundred cities." His poetic gift has outlived him, just as it survived all the ups and downs of his life.