There are two different angles to this problem: 1. The heat pump really is blowing cold air. Or 2. The customer thinks it is blowing cold air.
The second one quite often happens with first time heat pump owners. It is a simple mistake, - so we will tackle this one first.
Heat pump air is not as hot as the gas or oil furnace air that most customers are used to. Furnaces tend to put out air that is about 130 to 140 degrees. A heat pump running on first stage on a day that is 35 degrees outside, (depending on the return air temperature) might only put out 92 degree air. On a 20 degree day, it might drop to 85 degrees.
Well, this is less than body temperature (98.6 degrees) so it feels like cold air. It is still warmer than the house so it will still heat the house. Unlike a furnace that puts out a lot of heat for short periods of time, a heat pump will put out less heat for longer periods of time and do it more efficiently.
So if you are new to heat pumps, try measuring the air temperature with an accurate thermometer at the supply register before calling for service. If there is less than 15 degrees difference between the return temperature and the supply temperature then there may be a problem.
Now, what if the heat pump really is blowing cold air? In other words, it's not putting out any heat at all. Well this could be one of several things. Sometimes it could even be running in the air conditioning mode due to a malfunction such as a faulty reversing valve or thermostat.
Below is a list of possible causes. Items in blue usually require a service call. Items in red however can be addressed, even fixed by the homeowner.
Outdoor unit iced-up - weather related
Leaves, debris or snow against outdoor unit
Outdoor unit not running
Cold return temperatures - example: air handler in attic and return trunk disconnected from unit, pulling in cold attic air.
Unit in basement with a basement return and open windows or a flapping dog door stuck open.
Thermostat set below 65 degrees.
Faulty or poorly installed ductwork causes big problems for heating systems, and especially for heat pumps.
Return duct leakage
Low refrigerant charge
Refrigerant flow-related problem - restriction/bad metering device