According to the "book", the switch is a combo high pressure/low pressure/normal switch. The reason the compressor needs to be off with low temps is to prevent the compressor from trying to compress liquid refrigerant. also called "slugging". The suction of the compressor should only see refrigerant in a gaseous form. If it is 20 out and your car is cold inside and out and the compressor comes on immediately, I would suspect a faulty switch. On rotary compressors slugging is tolerated a little but puts a huge drag on the drive belt and will eventually damage the comressor. Like liquid gas in the cylinder of your engine, liquid refrigerant is uncompressable and removes the oil film from the walls of the compressor. If we have a gear type, the gears wear out fast, if we have a blade type, the blades wear out fast. Best way to check is with pressure gages and monitor the system pressures. The dash switch will keep the compressor off well enough though.
