Are you sure the air is cold? That is to say, are you sure the air isn't just 'slightly warmer than ambient'? I've seen systems where the air blown in from the heaters was only a couple of degrees up from ambient. Couple that with the fact that it's moving, and you'd stick your hand in the airstream and it felt kinda cool.
The real test is: does the HVAC system heat the house! Try turning the heat to a few degrees above exterior temp and wait a few hours - does the house get warmer overall, or colder? If it gets cool at night in your area, try the experiment at night.