I would imagine not being that you live in Arizona, but Im not sure what kind of temperatures you experience since I guess it would matter would part of the state you live in. It also would make a difference in what kind of quail it is that you have. What kind do you have and what will the temps be in mid-winter in the part of the state that you live in? Those 2 questions being answered should help someone give you an accurate answer.
If temps are going to get below freezing at any time, it is always best to offer up your quail a place to get out of the wind, rain and or snow. Something with walls, a ceiling and a solid floor. Put some bedding on the floor so they can keep their feet warm and off any wire. They can live thru some brutal cold temps, as long as they are dry and out of the wind.
I put an electric dog waterer in my large quail pen here in Montana. Put a layer of dirt and slipped it into the hutch I made to keep them out of the rain and now snow. They sure love it and huddle in there at night and when the wind blows. It's 28 degrees now and should drop to 19 tonight. They seem OK and are eating and getting warm water in the mornings. If it gets too bad, I may have to catch them and put them in the garage in a smaller pen.