Should I add a return air vent in a refinished basement?
Yes , add at least 1 return at or near the floor ( in the wall). All the cold air in the house heads to the basement since cold air is heavier than the warm air. In some installations a central return duct and grill is installed in a central location to reduce cost,( this has become the norm) but is only to save costs. Every room should have supply and return registers. you cannot push supply air into a room with out having a way for the air to get out, ( its like a balloon). If you have a central return grill you normally need to have the bottoms of the doors shaved to allow the extra supply air to flow out. If you do not do this then the room will not receive enough air to cool or heat depending on the time of the year