All fuel burning devices need an air supply. In the case of direct vent appliances, there is an air intake to be plumbed to the outdoors as well as an exhaust pipe. This assures that the appliance is not drawing air into the house through windows, doors, etc. defeating weatherization and sealing. The combustion chamber in DV appliances is closed and isolated from the room. Even a direct vent fireplace is completely enclosed to allow no air to enter from—or exit to—the room.
Direct venting is still largely the exception rather than the rule, though DV is gaining favor with many people who prefer higher energy and cost efficiency, so much new construction is now using DV.
A 1950s gas water heater has an air intake, but it simply draws air from its surroundings.
That water heater does not appear to be direct vent, so a general air supply for it is needed and the "floating beanstalk" air tube is a reasonable way to achieve ventilation—removing it would be "bad".
It occurs to me to try to decrease the chilling effect the intake causes for the room by moving it closer to the water heater, and maybe even "boxing it off" somewhat. However, if the outdoor air is very cold, like below -30°C/-22°F, and there is a lot of airflow, such an arrangement could damage the plumbing and tank by freezing water in the pipes, etc.
It all comes down to "working space", clearances, exhaust, and combustion air.
Working space is the unobstructed area around (usually in front of) an appliance, allowing access to service the appliance. This will some times be specified in local codes, and often spelled out in the manufacturer's documentation for the appliance.
Some appliances may have specific clearances specified in codes or manufacturer's documentation, to prevent the transmission of heat from the appliance to other (usually combustible) materials.
Fuel burning appliances require a supply of fresh air for combustion, which in most cases cannot be drawn from living spaces. Local codes and Manufacturer's documentation should also specify how much, and where this air should come from.
Some appliances require a means to exhaust byproducts, in which case the room will have to take these in to consideration. Exact exhaust specifications for each appliance can be found in local codes, and/or the manufacturer's documentation.
If a room is designed properly, it's possible to fit multiple appliances in a single room.
Best Answer
That's your fresh air supply for your gas appliances. Newer high efficiency appliances are directly vented so you don't have the cold air dumping directly into your home. But for older style gas appliances, you have to have a fresh air supply to your utility room for combustion.