Many people come to the Phoenix and Scottsdale area during the winter holidays, and especially for several major events that are usually held toward the end of December and beginning of January. Before I give you the weather details, I'll provide the generalizations.
On New Year's Eve and New Year's Day it does rain from time to time, but it is not usually our wettest time of year. While it might be cool or cloudy, chances are that it won't rain on the morning of the Fiesta Bowl Parade. For the Fiesta Bowl, and in the years when BCS is played in Arizona, the stadium has a retractable roof, so weather is not an issue. For outdoor events like Buffalo Wild Wings Bowl (formerly known as the Insight Bowl) and the New Year's Eve Block Party in Tempe, weather will be an issue.
Does it ever snow? Yes it does, but usually not in a measurable way in the Valley, where Greater Phoenix is located. On the outskirts of Phoenix you may see snow for short periods of time -- just enough to make driving hazardous as everyone drives looking skyward!
Does it ever freeze? Yes, it does. While we don't have much of a variation between night and day temperatures during the summer -- it might still be over 95 in the middle of the night -- we have a wider range of temperatures during the winter months. Parts of the Phoenix area will see freezing temperatures at night, such that cars and plants may have frost on them in the morning, while daytime temperatures may warm up by 40 degrees or more! You'll be happy to know, though, that overnight freezes usually occur in the wee hours of the morning, and the outdoor events on New Year's Eve will have ended by that time.
Aside from watching football, participating in New Year's Eve celebrations and attending parades and classic car auctions, December and January usually are great months to get out and about during the day for jeep rides, horseback riding, hot air balloon rides, hiking and other outdoor activities. Wear layers in the morning and peel them off as the day warms up.
Be aware that as you travel up north to Sedona, Flagstaff, the Grand Canyon and beyond that the weather is very different. Those destinations are at higher elevations and they experience true winter weather. Dress appropriately and be prepared for winter driving conditions.
Now...the details! the primary source for the following data is the National Weather Service and covers data collected from 1895 - 2010. All temperatures mentioned are Fahrenheit.
December 31 / New Year's Eve Weather in Greater Phoenix
Average high temp for December: 70January 1 / New Year's Day Weather in Greater Phoenix
Highest average temp on December 31st: 65
Highest average temp in any single day in December: 71
Average low temp for December: 44
Lowest average temp on December 31st: 36
Lowest average temp on any single day in December: 34
Highest maximum temp on December 31st: 79
Highest maximum temp on any single day in December: 87
Highest minimum temp on December 31st: 56
Highest minimum temp on any single day in December: 60
Lowest maximum temp on December 31st: 47
Lowest maximum temp on any single day in December: 43
Lowest minimum temp on December 31st: 22
Lowest minimum temp on any single day in December: 22
Most rain ever on December 31st: 0.8 inches
Most rain on any single day in December: 1.5 inches
Average high temperature for January: 67
Highest average temperature on January 1st: 67
Highest average temperature in any single day in January: 70
Average low temperature for January: 45
Lowest average temperature on January 1st: 36
Lowest average temperature in any single day in January: 28
Highest maximum temperature on January 1st: 81
Highest maximum temperature in any single day in January: 88
Highest minimum temperature on January 1st: 58
Highest minimum temperature in any single day in January: 61
Lowest maximum temperature on January 1st: 47
Lowest maximum temperature in any single day in January: 39
Lowest minimum temperature on January 1st: 24
Lowest minimum temperature in any single day in January: 16
Most rain ever on January 1st: 0.22 inches
Most rain on any single day in January: 1.74 inches