My furnace duct system has a vent in the garage, right over the furnace. Is it necessary for the proper operation of the furnace to keep that open? I'd hate to waste the money heating up my garage, but I don't want to close the vent if it means damage to the furnace.
In the picture below, I have the vent closed, to increase the pressure going into the house.
It's not necessary, they probably just put it in because it was easy to do and gives you the option of heating the garage if you want.
I would keep the vent closed, and if you want an even better seal, the make magnetic pads that you can put over the vent as well
There is no reason to leave the vent open, dumping warm air into your uninsulated garage, unless you intend to do some work there on a cold day. Even then, it might still arguably be smarter to just bundle up.
Close the vent.
I'd leave it closed. I find that my furnace itself (located in the garage) keeps the garage pleasantly warm even with the garage vent closed. If the furnace was in the house, I might leave a vent open though (to keep the cars from leaking coolant from the hose/tube junctions, which they're prone to doing on those really cold days if not kept warm).
