What to wear and carry in Arizona:
Lip balm
Sun screen
Water
Hat
Sun glasses
Due to low humidity the air does not hold heat, so sunlight is the factor: in the day it can get hot, at night, cold; in the direct sun warm or hot, in the shade cool. So layers. When outside in the daytime you can peel and don as you go from sun to shade and back. Warmer clothes are needed after sunset for the evening and night.
Tucson is 10 to 15 degrees warmer, on average, than Sierra Vista.
In winter it can get cold here at night (not East coast cold, but cold) and our house is poorly insolated with high ceilings, so hard to heat.