If you do damage to the ice maker from freezing you will be in for a huge repair bill. I would get a gallon or two of antifreeze and properly winterize the unit...and run your fridge/icemaker until it's dropping "pink" cubes into the tray. Depending on model there is a way to disconnect the 1/4" line and run antifreeze directly to the ice maker so review your manuals. Not sure about the dishwasher but im sure its also critical not to freeze so protect it with antifreeze as it seems in storage running the furnace for several days may not be an option. Too many folks come on here after a freeze and wonder "what kinda damage do you think I did". I would do whatever I could to not be that person.
Yep...im paranoid about breaking stuff.