Well contrary to popular belief, Arizona isn't a giant desert. Arizona is one of the most diverse states in the nation when it comes to climates and landscapes. You can find nearly everything here except oceanside beaches or tundra.
For instance Flagstaff, Arizona is a college/ski town that often gets quite a bit of snow. Here's a picture:
Flagstaff (according to the interweb) gets an average of 110 inches of snow a year, areas of the North Rim Grand Canyon can get twice that! I'd be willing to bet on most days of the year, Flagstaff is colder than Chicago.
More fun facts:
Arizona has more pine trees than Massachusetts
Arizona has more mountains than Switzerland
Here are some more pictures of Arizona that those 'back East' probably wouldn't expect/belive: