Ac/heating unit not working properly. If the temp outside drops to around 40 degrees the unit will shut off and not come back on until temp outside rises to above 60

Possibly a tstat issue. Run system until satisfied, once satisfied indoor fan shuts down compressor still runs remove tstat face plate and see if compressor shuts down. Another issue could be a sticking contactor for compressor. With a meter you could check at the contactor to see if you lose your 24volts for cooling but contactor remains pulled in.

Heat pumps are designed to operate only with the heat strip if the outdoor temp drops below 50 to 53 degrees F. Heat pumps use the heat from the outside and transfer it to the inside, but if the temps outdoors do not hold enough heat, it ceases to function efficiently. Make sure the unit is always clean on the inside and on the outside coiling to make it as efficient as possible. I've been in the business for 17 years and around it my whole life and I've never recommended a heat pump for this very reason. They are only efficient in areas where the winter temps are more mild.

If you have a heat pump the compressor is locked out below that temp. If you have a dual fuel - hp/gas, the gas burners should come on as would the electric heaters if you have electric heat as backup.

sound like faulty out side air temperature sensor located center radiator support.

The fan switch is set to turn on at approximately 125 degrees and run until the heat exchanger temp drops to around 105 degrees. With age the sensitivity of this switch varies and summer heat can cause the switch to turn on if the outside temp is over 100 degrees. Only the fan is running, not the burner but you can shut off the power to the unit if this is an issue.

Heat pumps are the same as an A/C unit only it works in reverse. Instead of blowing cold air inside and hot air outside it blows hot air inside and cold air outside. The heat being blown inside is extracted form the cold air outside. Its called Latent heat Latin for hidden. Believe it or not even though its 20 degrees outside there is still heat in the air. Example if you want to drop the temperature of a freezer from 20 to 10 degrees you have to remove heat .I know your getting unusal weather and that is the problem. Heat pumps can only work no lower then around 20 degrees outside.Heat pumps are never used above the freeze line. With your unusal temperatures thats basically where you are now. Ride it out. When your temps rise a little your be fine. Im in Chicago.

If you have heat when its above 40 degrees most likely your problem is a bad thermostat, when it gets VERY cold out the engine cannot reach proper operating temperature to maintain heat quality because the thermostat is more then likely stuck in the open or partially **** in the open position....

Heat pumps only work down to a certain temperature, 35-40 degrees outside temp. Once it gets that cold the system cant pull any heat from the outside air and the aux heat kicks in to make up the differance.

Your outside unit is not defrosting. You need to call a service tech to check it out. Defrost board sensor or low on gas. Also you amy have an outside tstat that is not working correctly. Rus

When the unit does what you say does the fan motor outside stop also , if it does that means it is in defrost mode and should kick back over to normal after the system heats up the coil enough