A heating furnace may blow coldair due to the wrong thermostat setting, a dirty filter, dirty sensor or simply clearing out the initial cold air in the vent. It's not unusual for a furnace to initially blow cold air before heating up.
One problem with a malfunctioning furnace may be a dirty flame sensor. In the case of a dirty flame sensor, the air may begin heating for while, then turn cold. To repair a dirty flame sensor will require hiring a heating professional.
An additional problem with cold air coming out of a furnace could be the wrongthermostat setting. If the setting is only set to "fan," hot air will not come out of the furnace. The setting should be set to "auto" so the furnace will turn on with the fan.
Another reason the furnace may be blowing only cold air is that the pilot light for a gas furnace may be out. If this is case, simply re-light the pilot. If the pilot light continues to go out, more investigation may be required by a professional.
If the furnace is oil-heated and blowing cold air, the problem may be similar to a gas furnace malfunction and the filter may be dirty. Filters keep contaminants from getting into the air, and when itgets clogged, it also blocks the air from blowing through the vents.