Hot air is going inside and the cold air is outside

ok,

first the engine gets hot, if not there will no cab hot air.
so if you scan it the PCM shows the ECT reading over 180f,
does it. if not , the thermostat is bad.
in order !!!
blower works so not blower.
leaving dampers, does the HVAC self test pass?
if damper are in heat mode, that leaves only 2 left
(possible air filter there? ,its and option) in the dash HVAC box.
the heater core is packed. (in air side or water side)

fan defective or capacitor.

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.

Start the unit and go outside to see if the insulated pipe is sweating or cold, hot air should be discharging from top of outside unit. Since the breaker is not tripping, my best guess is the compressor is not operating. You might have to replace the capacitor.

If you can hear the compressor operating, then most
likely needs refrigerant

First check your air filters and make sure the inside and outside coil are clean. If they are clean and you are getting good air flow over the coils then you probably will have to get the unit charged.

Make sure it is in cooling mode. Sounds like you may have a problem with the reversing valve but you would want to check the pressures in the system first and make sure the charge isn't low.

Chances are you have a bad capacitor in outside unit. Take off cover to wiring. It is a oval silver cylinder. See if it is swollen or oily. If so replace, Also check for burnt wires on capacitor or contactor. Russ

It sounds like you have a unit called a heat pump. When a heat pump unit is in cooling mode the outside unit blows hot air and the inside unit blows cold air. If the outside unit is blowing cold then the indoor unit is most likely blowing room temperature or warm air. It sounds like the thermostat could be controlling incorrectly or you could have a failed reversing valve which is the device that switches the unit from heating to cooling mode.

Set thr thermostat to AC instead of HEAT.

Sounds like you have it in heating mode or it is low on charge. In cooling mode, the outside fan should blow hot air not cold.