Its not the ambient air that will disable the A/C compressor, its the thermistor in the evaporator. Though air temp does play part in it of course.No. The AC turns on with defrost to dehumidify the air in the car. Humidity causes condensation on the glass.
The AC won't run the compressor below 40-45 degrees F or some number around that. So if its cold outside, it's not running anyway.