Don't forget the combustion air is for all fuel burning appliances, not just the furnace. The water heater and possibly your clothes dryer also need combustion air. Yes, it is counter efficient, but not providing combustion air risks carbon monoxide poisoning. Not good!
One viable alternative would be to adequately heat the space, but that is certainly not efficient. It appears you could easily enclose the water heater and furnace in a utility closet. Be sure to determine the needed clearances and working access for each appliance and ensure they are maintained. AFAIK, the mechanical code often applicable in the US still requires two combustion air openings, one high and one low. You should verify your local requirements to ensure everything is correct. This is not the area to cut corners.
Even with the closet containing the cold air, if you have a gas clothes dryer, it still needs adequate combustion air. You would probably need some vents out of the closet to maintain this, but they can be relatively small, so the enclosure would still largely contain the cold air. Again, check your local requirements to determine the minimum vent area required for a dryer.
You would want to insulate the closet walls, and maybe even consider using an exterior door for access, as it will provide better insulation and weatherstripping to limit infiltration. OTOH, an undercut interior door might be adequate for dryer combustion air provision. You have a little research to do.
Your best bet is to refer to the owners manual of the furnace. The manual will tell you how long the vent can be and the maximum number of bends.
When it comes to C02 I get really nervous and venting is important. Call A pro. It should not be a hard job.
Best Answer
Is the feed cable a metal-sheathed (aka BX) cable? If so, the metal sheathing is likely providing a ground even if there are only two wires (hot and neutral) inside the cable.
It's also possible that the metal ductwork attached to your furnace is grounded at some point. This might be done in a reliable, intentional way, or it may just be that it comes into contact with some metal pipes somewhere.
I think it's unlikely that the concrete floor is providing such a reliable ground, and it's definitely not the way you want to do it -- the whole point of having a ground conductor is to provide a lower-resistance path to ground than the one that goes through your fingers to the floor you're standing on.
In any case, there ought to be a ground conductor to the metal housing of your furnace. The best way to achieve this would be through any cables feeding electricity to your furnace, but you may also be able to add a dedicated ground wire. I'd recommend checking your local building code to ensure any change you make is compliant -- things get complicated when you're dealing with HVAC and basements. Good luck!