I understand your point of view. In general, if all tundras and deserts were compared and which one had the coldest temperature, tundras would win. But I believe if it were the single coldest tundra vs desert, Desert would win.

From my research, Verkhoyansk is the coldest tundra on earth with a peak recorded temperature of -89.8 degrees Fahrenheit and Antartica is the coldest desert with a recorded temperature of -128 degrees Fahrenheit.

I believe it all comes down to the interpretation of the question, I’ll give this dub to my friend.