How can I avoid cold rooms due to combustion air intake?
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.