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Any small openings that let the heat out of a house represent a significant amount of heat loss and wasted money. Doors, in particular, are notorious for letting heat escape.
To winterize your doors, start by tightening the hinges and checking for any cracks in the door frame that might let the warm air escape. Use caulk to seal what you find.
You can also add something to the bottom of the door to stop drafts. Inexpensive options include a door sweep, which attaches to one side and has a flexible piece that hangs below the bottom of the door; a double draft stopper, which slides under the bottom of the door and has cushions on either side; or a door sock, a roll of fabric that is placed along the bottom of the door. For a bang for your buck, you can make a door sock by rolling up a towel.