Besides what Steve said you could also insulate and heat the garage but then you would be looking at a new heater for the garage since you couldn't run a return or duct out there and any extra btus available for heating should go in the rooms upstairs.
Your floor above the unheated garage acts just like an interstate overpass, the cold air underneath allows it to ice/freeze up first before the rest of the roadway. Best bet is to put in a drop ceiling with some r-30 fiberglass batt insulation and follow Steve's recommendation about adjusting or adding vents provided you have the furnace capacity. By the way, what is the insulation like in your walls? Last but not least, don't do anything that would somehow allow car exhaust to get into your air ducts or your air returns. Carbon monoxide kills. Put a wood burner in the garage for those really cold rainy nights in Georgia.