There are two parts to this problem.
The second one usually happens with new heat pump owners, it happens often, and it is easy - so we will tackle this one first.
It is quite simple. A heat pump puts out much cooler air than a gas or oil furnace that most customers are used to. Furnaces tend to put out about 130 to 140 degree air. A heat pump running on first stage on a 35 degree day, depending on the return house temperature might only put out 92 degree air. On a 20 degree day, it might drop to 85 degrees.
Well, this is less than your body temperature so it feels like cold air. It is still warmer than the house so it is still putting heat into 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.
So if you are new to heat pumps, try measuring the air temperature with an accurate thermometer before calling for service. If there is no difference between the return temperature and the supply temperature then there is 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 several things. Sometimes it could even be running in the air conditioning mode due to a malfunction.
Below is a list of possible causes.