Hot Deserts and Cold Deserts – Deserts can vary in temperatures of extreme heat and extreme cold but both have very low rainfall
NOTE: Hot or Cold temperatures do not determine whether land can be classified as desert. It is determined by the fact that the area has very low rainfall and the area is barren.
HOT DESERT – VERY LITTLE RAIN
COLD DESERT – VERY LITTLE RAIN
The term "hot desert" hints that there are also cold deserts, and vice versa. This suggests that the definition of deserts doesn't depend on temperature.
DESERTS = very low rainfall and barren areas
The factor that determines if land qualifies as a desert is:
250mm or less of rain per year
When it snows in cold deserts like the Arctic, the snow does not melt but becomes the ground. However even if you melted it, there would still be less than the equivalent 250mm of rain per year, so this would be classified as a cold desert.