The region would be South America.
The Atlas Mountains act as a barrier, blocking moisture that would otherwise reach the Sahara desert from the north. This rain shadow effect of the mountains contributes to the arid conditions in the Sahara region.
The Atacama Desert falls under the cold desert biome. Despite its location in a subtropical region, the Atacama Desert's high elevation and surrounding Andes Mountains contribute to its unique climate, characterized by cold temperatures and low precipitation.
That would be the Atacama Desert in northern Chile.
The Chihuahuan Desert of west Texas would be the closest.
It would be a semiarid grassland or steppe.
The El Paso region in Texas is typically associated with a desert biome, specifically a hot desert biome. This is characterized by low precipitation, high temperatures, and sparse vegetation, including cacti and drought-resistant plants.
Snow is a rarity in southern Arizona so would be seen on the mountains only after a rare winter snowstorm in the Sonoran Desert. It would quickly disappear, however.
El Paso, Texas
Antarctica is a polar desert.
In the Sahara desert you would only find animals at an oasis.
An impossibility - the equator is in the tropics and that region receives to much rain to have a desert.