Heat Pump Min Outdoor Temp for Goodman GSH130361AD
From personal experience, most R22 heat pumps like the Goodman GSH130361AD do not produce much heat below an outdoor air temperature (OAT) of 35F and the system coefficient of performance drops such that running much below that OAT is not very helpful.

The main concern with low temperature heat pump operation is excessive compressor discharge temperature.  As the OAT drops relative to the indoor air temperature, the compression ratio increases causing higher heat of compression and reduced coolant flow through the compressor.  Discharge temperature should usually not exceed 200F and in no circumstances be higher than 215F.

If you are really dedicated to finding the safe low temperature operating limit for your system, strap a wireless thermometer on the larger refrigerant line where it exits the cabinet of the GSH130361AD and monitor the temperature from inside your home on cold days.  When you see the discharge temperature climb to 190F, you will know you have reached the OAT low temperature cut-off.

EDIT:  Since I suggested measuring the discharge temperature outside the cabinet instead of 6" away from the compressor, I lowered the temperatures to 215F and 190F to give a margin of safety (vs. the original 225F and 200F temperatures I mentioned).