Antarctica is considered a desert and not tundra. Antarctica is actually the driest continent on earth, and of which, a good larger part of it is a desert. The continent does not have much rain or snowfall on it, but it is a very cold place, and thus, the little amount of precipitation that might have fallen on it does not really melt.
Its annual precipitation might not be more than 51mm, considering the interior. Antarctica is the most isolated place in the whole world, and it is very cool, with a high amount and speed of wind blowing.
The continent has its face covered by an ice sheet, which seems permanent, and contains about 90% of the freshwater of the earth's water body. This ice sheet is formed due to the freezing ocean that surrounds the continent. Hence, the Antarctica continent is a wet or cold desert and not really tundra.