Yes, it can snow in the desert, in fact, snow has fallen in almost every part of the United States at one time or another.
The most snow ever reported in Phoenix, Arizona, was 1 inch (2.5 cm), an event that has happened there twice, the first time on January 20, 1933, and the second time exactly 4 years later to the day.
More than three fourths of the surface water supply in the western United States comes from melted mountain pack snow.
