As spied by Multiplayer First (which wrote up a handy-dandy guide for how to find it), the Easter egg sends Riley streaking across the sky at the head of Santa’s sleigh, with Capt. Price in the jolly old elf’s seat.
As a bonus, there’s a vague Back to the Future reference to trigger the whole thing. It’s on the new Winter Docks map (basically the Docks map tricked out with holiday decorations). Find the clock atop the big warehouse outside — it looks like the Hill Valley Courthouse’s clock from the movie.
When lightning strikes the clock (MP1st tells you how to cause that) Riley the Red-Nosed Reindog’s flyby will begin. Multiplayer First notes that the Easter egg may be triggered in private matches, too, so you can set one up and see for yourself right now.
Call of Duty Dog rocketed to stardom when he showed up in an announcement video for Ghosts that showed Infinity Ward animators’ scrupulous attention to detail. Riley (dog actor’s name: Colin) became a day-zero meme, and was last seen on the product packaging for the Actibase console inside a shot-up electronics store in Call of Duty: Modern Warfare’s campaign.