Does wind chill work in deserts?
As you state, wind chill "is the cooling of a body due to the passing-flow of lower temperature air.

Because of this, wind chill only occurs when then air had capacity to absorb heat from a body - thus chilling the body. The capacity of air to absorb heat from a body is dependent on the temperature difference between the air and the body, and the humidity of the air.

In determining the ability of the air to absorb heat , the wet bulb temperature must be used, in conjunction with the dry bulb. Wind chill and [heat index] (https://en.wikipedia.org/wiki/Heat_index) are related.

In a hot environment, such as a very hot day in a desert, a wind chill factor usually will usually not exist. Under such conditions is it possible to a body to over heat and experience heat stress and hyperthermia, which can lead to death. Also, one has to be careful so that wind burn doesn't occur.