Yes — it does get this cold in northern Arizona from time to time. Not often, though.
This morning (01 January 2011) the temperature fell to -30°F in Bellemont, Arizona, where the National Weather Service office is located. At the Flagstaff airport it reached -19°F and the Grand Canyon National Park airport fell to -28°F. Even colder was the automated site at Greenbase, located between Williams and Parks, which fell to an astounding -38°F.
The record for this date in Flagstaff is -21°F (1919) and the coldest temperature ever recorded in Arizona is -40°F at Hawley Lake (07 January 1971).
So what can you do when it is that cold outside? Well, you can toss a cup of boiling water in the air to see what happens!
First, the boiling water flashes to steam then the vapor freezes into small ice and snow crystals. For some detailed explanation of how this happens, check out these two links:
By early afternoon, the temperature had risen to 25°F resulting in a range of 55°F in just a few hours!