Does my mechanical room need ventilation to the exterior?
Air is a thing.  (This took humanity millenia to figure this out; we figured out industrial use of fire soon after, and then, aviation!) You can even put air in a bag, that's what a bag of air is!  

Fire involves fuel (you bring) and air (that is just around).  Your furnace and water heater burn a fuel, and get air from somewhere.  Where they get it is very important!    Some furnaces use "direct vent", meaning they bring in fresh air from outside, just for their own use, using a double exhaust pipe.  Those you don't need to worry about.   However most simply grab air that is in the room, and that's a problem.  

For every bagful of air that the furnace or water heater send up the stack, a replacement bagful of air has to come into the house somehow.   Back in the day, houses were very leaky, and that wasn't a problem, but modern houses can be tight enough to make that a problem.  

Regardless, one problem is the replacement air leaking into the house is cold and dry (or hot and wet), causing drafts and forcing the heater and humidifier (or A/C) to work all that much harder.  

Ventilating the equipment room would be a step in the right direction, becuase it would provide combustion air for them without pulling drafts in the rest of the house. You may also want to insulate this room from the house -- but not too much.... on a very cold day, that could be a lot of cold air.  You have to make sure the water pipes don't freeze!  

In an ideal world, you have direct venting, where the outside draw air goes directly (and only) to the burners.