Just bear in mind that there is no high elevation part of the southern Arizona mountains that is more than about 8 trail miles from lower, desert, elevations. You can usually walk out of the snow in 3-4 miles if you decide to bail. It may still be cold and wet lower down but I'm sure you are accustomed to that in Georgia. It can get icy on the trails so you will want some sort of traction appliance with you. And, usually, the snow is not deep enough along the AZ trail part of the mountains to stop you; I have never had to deal with more than ten inches in the ten years I have been hiking around here. You can get wet feet from it so have a spare pair of socks to change into at night. You can encounter some high winds. As I write this in my rural desert home, the wind is gusting to 30 mph outside. I am sure than it is closer to 50 mph in the mountains. Have a good wind proof top and bottom and consider something to cover your face such as a Balaclava. A pair of light fleece mittens would also be of use; mine weigh about an ounce and have kept my hands warm in some pretty miserable weather. The neck gaiter is a good idea. A tent is a better option than a tarp for the weather you might encounter; tents are better in wind.
May I walk in beauty.