Most of the items in this checklist below you can address yourself but it is always better to have a trusted contractor or a handyman to help you to ensure proper maintenance.
Weather Stripping and caulking
Look for any gaps that can allow the cold air to travel inside your property. Weather stripping is one of the most important things to be addressed. Sometimes, weather stripping is not just enough, look for any other areas with gaps and seal them with a proper filler/caulking. Apart from doors & windows, look for gaps around pipes coming through walls, Vents, Fans, AC Units etc.
Prevent Freezing of Pipes
Pipe burst can cause thousands of dollars in water damage. When water freezes, it expands and puts tremendous pressure on pipes to make them burst.
Obviously, maintaining proper temperatures (not allowing to reach freezing temperatures) even when you are out on a vacation will help prevent any issues.
Insulate the pipes. Use rubber/fiberglass sleeves to wrap around the pipes.
Let faucets drip in severe cold spells.
Check and Clean Attic Ventilation, Gutters, Downspouts
Check all vents for dirt, dust, and leaves. They can be cleaned with heavy water or air pressure (once again, it may be a better idea to use a Pro for few such items). While cleaning with water, make sure not to saturate the insulation with water!
Poor attic ventilation can cause lots of issues like ice dams, mold, increased heating requirements and reduce the life of shingles.
Put a hose into downspouts and run water under pressure as much as possible to see if there are any clogs. If you find that water doesn’t flow smoothly, use a snake to remove the clog.
Check your heating system
It is a good idea to have a maintenance contract with a good company and then let them take care of all checks. You may have to replace the filter in your furnace and do a test run before the cold weather strikes!
Winterize outdoor faucets, sprinklers, and equipment
Drain the hose, detach it from outdoor connections. Close shut off valves serving outdoor faucets. Drain your irrigation system.
Fireplace and Chimney
Even if you are not using your fireplace, you should get the fireplace and chimney professionally checked and cleaned. Debris inside chimney can cause a fire risk.
Drainage in surroundings
There are possibilities of water damaging your foundation if there is improper slope or pits surrounding your foundation walls. Freeze and Thaw not only affect your pipes but can damage the walls and foundations too. Any exterior repairs in paving / proper rain drain shall be checked and addressed in advance.
Replace screen panels in Doors & Windows to storm panels
Obviously replacing single panels of screens with storm panels will help but more layers of glass also mean more protection. Having double glass units/panels will help save on energy consumption too.