The general perception is that Arizona being mostly desert, is rather warm.  While that is true of the lower elevations in the state 9and in the West generally), much of AZis 5000 feet or higher and it can get really cold.  I have recorded minus 30F on an official Weather Bureau thermometer and have experienced -40 at really high elevations on the San Francisco Peaks.  Even in Tucson, winter lows will dip into the 20s.  The dry climate means larger diurnal temperature swings.