Was this damage to the ceiling caused by heat from a water heater vent

Yikes, this is really the first time I have ever heard of this configuration. Could this have been part of a previous central forced hot air system? It is not common to tie exhaust vents from a bathroom to any other living space. A dedicated exhaust fan vented to outdoors with a one way damper is a very important way to remove excess moisture from bathrooms and help prevent mold and mildew growth. It is not acceptable to vent a bathroom to another living space or into an attic. It is equally not right to tie this type of vent to any other air plenum. If you are feeling cold outside air through these vents, you are getting huge heat losses. There is no need to introduce outdoor air into your house intentionally unless it is done with specifically designed air exchange equipment in an extremely airtight designed house. I think you need to determine the routing of these "phantom" vents and come up with a plan to isolate the bath vents to the out of doors with a proper bathroom fan unit and block your heat form other areas from being wasted out an open plenum.

If the furnace and water heater are gas powered, it would be to provide adequate airflow for their combustion so that you don't get carbon monoxide forming in the utility room.

Here's a link with some information. An excerpt:

The heating appliances are fully isolated from the living space with partitions. Figure 1 provides two vents to the outside, one within a foot of the ceiling and one within a foot of the floor. If vertical ducts are used to bring combustion air to the appliance each vent should be sized at one square inch of free vent area per 4000 BTUH of the appliance input rating.

(This is based on a half-remembered long-ago conversation with a service person working on my furnace and heater, which are in the center of my mostly-unfinished basement: I mentioned framing in a utility room around them and he said not to for that reason).