In winter you are probably going to be in the southern half of AZ and the southern third of NM. The Border Patrol has a strong presence. There are road blocks and lots of Spanish culture.
Phone service will be erratic. You can travel around and find a high spot and usually get service with some effort, but don't count on it all the time. Diesel and propane are available lots of places. Firearms are easy to carry in NM and AZ.
In the bush in the SW you have to learn to size up people. It is sometimes hard to tell the difference between ranchers, ag people and those running drugs from Mexico. Do you speak any Spanish? Do you understand Mexican culture?
At one time Quartzite was the place for rocks and gems. Most of that activity has moved to Tucson. Now it is just a gathering of RVs in the middle of nowhere with few amenities and a lot of people.