In Arizona, there are some reliable water sources but they may be further up in altitude. As you go up a desert mountain, you may actually get into forest/alpine biome. Here's Reavis Falls a bit off trail in the Superstitions near Phoenix in January ...
There's water but also notice the ice form. Reavis ranch (long abandoned and donated to the USFS), the upstream source of these falls, we had overnight temps in the low teens, then down stream the temps were upper 20's/lower 30's. Dayhiking from camp, it got colder and that's where we found the semi-icy falls. Neat ecology as the trail goes from desert to chaparral to forested and neat history if you read about Reavis growing apples for Phoenix around the 1900's.
Add: as we were leaving a large Scout troop was just coming off-trail so realize these cities are populated and you will run into other scout troops, college outdoors programs, etc..
There's some water in east Sagauro near Tucson and don't forget the nearby Catalina mountains which is USFS. The latter can be kind of cold and slightly damp near water sources in fact.