There is no distinct "Arctic Desert". The correct term is polar desert, which encompasses the high-latitude regions of Antarctica, Greenland, and the Arctic islands (e.g., Canadian Arctic Archipelago, Svalbard, Franz Josef Land).
Polar deserts are defined by extremely low precipitation (typically <250 mm/year), not temperature. Despite being ice-covered, they receive minimal snowfall, making them deserts in the climatic sense.
The exact area of the polar desert biome varies by definition (e.g., precipitation threshold, vegetation criteria). Estimates for the Arctic polar desert alone range from 2.6 to 5 million km², while the Antarctic polar desert covers ~14 million km².