Our electric furnace is set at 73 degrees. When the furnace comes on it runs great, until it reaches the 73 degrees. Than the furnace part shuts off and the fan continues to run until the temperature is down to about 70! My husband keeps saying it's because it is so cold outside, but today it was about 45 and it still did it. He tells me the colder it is the longer the fan will blow once the furnace shuts off.

Is this true or is something wrong?

Usually on a electric furnace the blower is on a timed cycle that is controlled by a sequencer. The sequencer could be going bad causing the long blower run time.