Which is the largest cold desert?

Antarctic desert (aka Antartica)

Explanation:

The Antarctic Desert is the largest desert on Earth, measuring a total of 13.8 million square kilometers. Antarctica is the coldest, windiest, and most isolated continent on Earth, and is considered a desert because its annual precipitation can be less than 51 mm in the interior. It’s covered by a permanent ice sheet that contains 90% of the Earth’s fresh water. Only 2% of the continent isn’t covered by ice, and this land is strictly along the coasts, where all the life that is associated with the land mass (such as  penguins, seals and various species of birds) reside. The other 98% of Antarctica is covered by ice which averages 1.6 km in thickness.