Yes, it does snow in Arizona! In my younger days, I thought that all of Arizona was hot and dry. Flagstaff, Arizona is at a fairly high altitude and gets quite a bit of snow during the winter as you can see from some of these slides. Much of Arizona is actually forested and, at the higher altitudes, looks like this slide during winter.
The photos in this slide show were taken in the mid-1990's by Steve Grande on his Amtrak travels throughout the nation. The size of the photos is purposely smaller as disk space was expensive and download speeds were slower at that time.