Heaters: Replace filters in heating units (including water heaters); prepare to do it monthly. For water heaters, clean out sediment at the base of the tank. Make an appointment with an HVAC professional to come and check the furnace before you begin using it. Then, once any fixes have been made, go room to room and adjust vents so that each room heats evenly.
Exterior Windows and Doors: Windows are an obvious weak point to the elements. Check the caulking around the edges, repairing any spots that look worn, and replace broken panes. If you don’t have blinds or drapes on your windows, consider investing in window insulation film—a plastic insulation that is applied by sticking it to the glass and using a blow dryer to shrink it. (One disadvantage is it gives the window a cloudy look, but it can substantially prevent cold from creeping in.) For doors, check out your threshold and see if it needs to be replaced. If your doors seem particularly vulnerable, consider installing new weatherstripping.
Pipes: Insulate pipes before temperatures reach freezing, using foam rubber sleeves or fiberglass insulation. When cold temperatures hit, always be on the lookout for signs that pipes may be freezing, such as water pressure going down.
Carbon Monoxide Detectors: Install one near your furnace and water heater. The increased use of heat during the winter raises the probabilities of heating problems, so prepare for all eventualities. Also make sure to check all smoke detectors.
Roof and Gutters: Check roof for weak spots, and replace broken or worn shingles (paying for shingles is better than paying for water damage). Clean out gutters, making sure to do one last sweep after all the leaves have fallen, and check that gutter direction will not create ice patches in walking areas around the house.