"Winter is here": promotional material for the new season.
But yes. Winter is here. Both in the books and the show.
ADWD epilogue (obvious spoilers)
The snow had finally stopped falling. Behind a veil of ragged clouds, a full moon floated fat and white as a snowball. The stars shone cold and distant. As Ser Kevan made his way across the inner ward, the castle seemed an alien place, where every keep and tower had grown icy teeth, and all familiar paths had vanished beneath a white blanket. Once an icicle long as a spear fell to shatter by his feet. Autumn in King's Landing, he brooded. What must it be like up on the Wall?
The door was opened by a serving girl, a skinny thing in a fur-lined robe much too big for her. Ser Kevan stamped the snow off his boots, removed his cloak, tossed it to her. "The Grand Maester is expecting me," he announced. The girl nodded, solemn and silent, and pointed to the steps.
Pycelle's chambers were beneath the rookery, a spacious suite of rooms cluttered with racks of herbs and salves and potions and shelves jammed full of books and scrolls. Ser Kevan had always found them uncomfortably hot. Not tonight. Once past the chamber door, the chill was palpable. Black ash and dying embers were all that remained of the hearthfire. A few flickering candles cast pools of dim light here and there.
The rest was shrouded in shadow … except beneath the open window, where a spray of ice crystals glittered in the moonlight, swirling in the wind. On the window seat a raven loitered, pale, huge, its feathers ruffled. It was the largest raven that Kevan Lannister had ever seen. Larger than any hunting hawk at Casterly Rock, larger than the largest owl. Blowing snow danced around it, and the moon painted it silver.
Not silver. White. The bird is white.
The white ravens of the Citadel did not carry messages, as their dark cousins did. When they went forth from Oldtown, it was for one purpose only: to herald a change of seasons.
"Winter," said Ser Kevan. The word made a white mist in the air. He turned away from the window.