Depends on what kind of system you have. The outdoor fan will run only if the system is a heat pump. If you have gas or strip heat (electric heating elements) the outdoor fan won't run. If the system is a heat pump, the outdoor fan normally turns off during defrost cycles, back on when defrost is finished.

dadoes, thanks so much for responding. It is an electric heat pump. I checked the unit for signs of ice but everything seemed fine. I turned it on today to see what would happen and the inside furnace kicked in and the unit outside started humming but the fan still didn't rotate. I looked for a reset switch on the outside unit and didn't see one. So, it's possible we just caught it during a defrost cycle and everything is fine?

No, the fan should run. It probably has what is called a 'bad contactor'. This is the relay that turns on the fan for the unit.

If you know how to set your thermostat to 'Emergency' heat (E), then you can do this until the service person comes and checkes the unit.

Thanks weedmeister. I turned it back on last night before going to bed on regular heat and the temperature was back up to 72 down there today. It's going to be a few days before the repair guy comes. What does emergency heat do differently than regular heat?

All heat pumps have (or should have) electric heating elements for supplemental/auxiliary and emergency heat.

Supplemental/auxiliary simply has the heating elements running at the same time as the heat pump to supplement it when outdoor temps are very low and it can't handle the heating demand by itself. The thermostat automatically triggers supplemental heat when needed, if the room temperature drops too far below the setpoint.

Emergency heat is a manual setting on the thermostat that shuts off the heat pump (compressor) and runs ONLY the heating elements. It's intended for use when a problem occurs, such as a failed compressor ... or condensor fan as in your situation.