At that outside temperature, it's probably a refrigerant leak. Leak needs to e located and repaired if possible. That in itself can be problematic. You should know the age of each system. Obviously with the condenser covered in ice, it was not putting out much heat if any.

IMO

I don't know what brand or model is there, but the heat pump in my former house did not initiate the defrost mechanism on the outside unit if thermostat set only to 'heat'. It had to be on 'Auto', meaning the setting to either cool or heat as needed to the called for degrees programmed into the thermostat. If set to heat only, the outside unit could frost up - visibly, significantly, in temps you describe - although I don't think I'd call it a layer of ice. The time it turned into a giant ice cube completely encased, it was freon and not a particularly expensive fix, only inconvenient. Christmas Eve as we were leaving town.

I mention this on the chance the home is vacant, and a realtor is operating an unfamiliar system.

"... the heat pump in my
former house did not initiate the defrost mechanism on the outside unit
if thermostat set only to 'heat'. It had to be on 'Auto', meaning the
setting to either cool or heat as needed to the called for degrees
programmed into the thermostat."

That is not how a heat pump is supposed to work. Defrost is a function of heating operation and should trigger when the thermostat's mode switch is on either Heat or Auto. Some thermostats don't have an Auto-mode position and they still operate a heat pump properly for heating.

Check to see if the indoor coil is frozen too. Most likely low refrigerant due to a leak at the evaporator (indoor) coil or condenser (outdoor coil). One (or both) may need to be replaced. If you're serious about the house, have the system checked and use this to negotiate the price.

Dadoes, just going by what the heating cooling company who sold and installed it told me. The thermostat (Honeywell) had Heat, Auto, Cool. Fan had Auto and Manual. Our summers aren't warm, I'd had the system off. In Fall when I turned it to heat only, frost on the outside unit. The service person told me it was because of my thermostat setting which needed to be on Auto to initiate the defrost mechanism. I followed their suggestions and used that system 25 years, efficient heating and occasionally cooling (Pacific Northwest, ocean side), before selling the house.

'The time it turned into a giant ice cube completely encased, it was freon and not a particularly expensive fix, only inconvenient.'

Not anymore. If the unit has a Freon leak, leak must be repaired. Freon (R22) is going away. Price increases will continue in dramatic fashion over the next few years. If the unit is an R22 Freon unit, your best option is to convert the system to new refrigerant R410a (requires equipment replacement).

What happened 25 years ago, is irrelevant. Welcome to 2016.

Yes, and I sold the house in 2014, wasn't exactly referring to an irrelevant childhood experience.

When I sold the house and during the disclosure and inspection process, I had the heating/cooling professionally inspected and a report issued that said all components functional, no service required. That was in response to the buyers inspector stating the electric back up furnace wasn't operational, when the problem was simply him not knowing how to turn it on.

That may make me a little sensitive to persons not familiar with the system making buyers home inspections, but of course has nothing to do with OP Bob and his original question. I hope if he really likes the house, finds no major or expensive issues. Carry on.

Here's the picture the inspector took of the iced up unit.

There are three outdoor units side-by-side for different zones in the house, the other two were ~10 years old, but this one was maybe 15 years old. Their Realtor said that they have already had a service guy come out who "fixed it" but I wasn't told what the problem was or what the supposed fix was.

Their realtor said that they have already had a service guy come out who "fixed it"

He probably just added R22 and left. If it's a leak, it'll just happen again.

I would ask for a copy of the service report...looks like a cheap low end old r-22 condenser...I doubt that unit has much more life...

IMO

By popular vote,freon leak it is I suppose ,there's no way it could be a problem with defrost, stuck contactor or half dozen other things that often frost up coils. It's amazing what conclusions can be drawn through a snap shoot and a few words. How long can it be before the interweb render's trained technicians obsolete and unnecessary? And the cherry on top? OP can use it to negotiate his real estate sales contract.

Sure Klem, call the interweb and have them come to your house to fix it.

Crystal Balls says: 'Don't worry Ray, your job is completely safe.*'

*Disclaimer: provided that flaming rock in the sky doesn't burn out.

Dadoes, just going by what the heating cooling company who sold and installed it told me. The thermostat (Honeywell) had Heat, Auto, Cool. Fan had Auto and Manual. Our summers aren't warm, I'd had the system off. In Fall when I turned it to heat only, frost on the outside unit. The service person told me it was because of my thermostat setting which needed to be on Auto to initiate the defrost mechanism. I followed their suggestions and used that system 25 years, efficient heating and occasionally cooling (Pacific Northwest, ocean side), before selling the house.

What thermostat are we talking about here. Some thermostats are not meant to be used with heat pumps. There is different thermostat wiring involved as well.