I am a native Arizonan (living in Minnesota - don't ask).
Temps in December can get chilly. There have been times where it didn't get out of the 40s during the day. It depends, and el Nino is going to play a part this year. It can be a bit damp, as well.
I remember getting a snow suit at Christmas, and actually needing it to protect me from the cold. Then again, I remember playing basketball in shorts a couple of Christmases ago while visiting Mom.
Bring a coat, sweaters and gloves. Be prepared NOT to use them!
Remember the Desert gets VERY cold at night. (i.e. 80 during the day, 20s at night).