arctic desert
From Glossary of Meteorology
"Any area in the high latitudes dominated by bare rocks, ice, or snow, and having a sparse vegetation and a low annual precipitation." [from Glossary of Arctic and Subarctic Terms (1955)].
Thus stated, this includes portions of both ice cap and tundra regions of both hemispheres. The term barrens is sometimes used, but this has more general application.
Arctic, Desert, Tropic Information Center (ADTIC) Research Studies Institute 1955. Glossary of Arctic and Subarctic Terms. ADTIC Pub. A-105, Maxwell AFB, AL, . 90 pp.