Luna: So, my little moon beam, how do you like Equestria?
 
Desert Moon: The sun feels different here, mama. Are we staying here?
 
Luna: Yes.
 
Desert Moon: Then its fine.
 

 
After the death of her sister, Princess Luna wandered the earth for a while. After a 2 years, she returned with little Desert Moon in tow. Apparently, while Luna was in the deserts of a faraway land, she met a Sphinx and copulated. From their union, Desert Moon was born.
 
Sphinx’s are creatures of the desert and the sun, so their coats shift to match the time of day to ensure their survival. Desert Moon, however, is different. Only her mane changes color and the color is always the opposite to the time of day. Her mane is pitch black during the day and the color of sunset at sunrise. At night, her mane is pure white.