There is an Antarctic Desert but no Arctic Desert. The Arctic is mostly open sea, frozen sea ice and tundra.
There is one Arctic desert. It is the Arctic Circle. Top of the world.
The Sahara is the largest non-arctic desert.
Most scientists do not recognize an Arctic Desert. The Arctic consists mostly of sea ice or areas of tundra - a distinct biome that differed from a desert. Antarctica, however, is recognized as a true polar desert.
The Arctic desert is 14.0 kilometers big. This the 5th largest desert in Asia.
The Sahara is the largest non-arctic desert.
If this is a deserted Island this is strictly a practical consideration. If this is an Arctic Island you will need heavy Arctic clothing If this is a tropical Island you will need clothing to protect you from insects, damage from the environment depending on what you need to do to survive. Shoes for example. Of course a Desert island would be different ;)
You could survive in either desert, given the appropriate supplies, clothing and transport.
The Arctic is primarily sea ice, open sea or tundra and not classified as a true desert. However, people do live in the Arctic.
Arctic desert (Russia)
The Atlantic is an ocean and not a desert. Most of the Arctic is sea ice and not a desert. Those parts of the Arctic on land are considered as tundra and not desert. They share some similar characteristics but are separate biomes.
There is no 'Arctic Desert.' The Arctic is primarily sea ice with some land areas of tundra. While tundra shares some characterisitcs with the desert, it is a different biome. Antarctica, however, is true desert and the coldest biome on earth.
The Arctic is not considered to be desert as much of the Arctic is sea ice or open sea and some tundra. Tundra is a distinct biome in its own right. The Gobi Desert is considered the most northerly.