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 Scottsdale and Phoenix 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 the College Football National Championship is played in Arizona, the stadium in Glendale has a retractable roof, so weather is not an issue. For outdoor events like the Cactus Bowl, the weather will be an issue.
Does it ever snow? Yes, it does, but usually not in a measurable way in the Valley of the Sun, 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°F 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 2000 - 2014. All temperatures mentioned are in degrees Fahrenheit.
December 31 / New Year's Eve Weather in Greater Phoenix
Average high temp for December: 68
Highest average temp on December 31: 64
Highest average temp in any single day in December: 71
Average low temp for December: 44
Lowest average temp on December 31: 32
Lowest average temp on any single day in December: 32
Highest maximum temp on December 31: 74
Highest maximum temp on any single day in December: 87
Highest minimum temp on December 31: 51
Highest minimum temp on any single day in December: 60
Lowest maximum temp on December 31: 48
Lowest maximum temp on any single day in December: 37
Lowest minimum temp on December 31: 22
Lowest minimum temp on any single day in December: 32
Most rain ever on December 31: 0.1 inches
Most rain on any single day in December: 1.5 inches
January 1 / New Year's Day Weather in Greater Phoenix
Average high temperature for January: 67
Highest average temperature on January 1: 65
Highest average temperature in any single day in January: 70
Average low temperature for January: 45
Lowest average temperature on January 1: 42
Lowest average temperature in any single day in January: 29
Highest maximum temperature on January 1: 81
Highest maximum temperature in any single day in January: 86
Highest minimum temperature on January 1: 53
Highest minimum temperature in any single day in January: 61
Lowest maximum temperature on January 1: 46
Lowest maximum temperature in any single day in January: 41
Lowest minimum temperature on January 1: 30
Lowest minimum temperature in any single day in January: 29
Most rain ever on January 1: 0 inches
Most rain on any single day in January: 1.74 inches