A/C not only cools, but also drys the air. When you have the defrost on in the winter, you usually have the temp knob on warm and it blows warm air regardless of whether the A/C is engaged. But that warm air is dry, thanks to the A/C, and lets the defrost work more efficiently. Blowing humid air doesn't work as well when attempting to defrost, even if it's warm.

Also, there is a temp sensor. Here in MN it gets cold enough where the A/C won't kick in. The colder the air is, the less moisture it can hold, so there's no need to dry the air when it's really cold. I'd be willing to bet you won't likely see temperatures cold enough in Tucson where the A/C won't engage.