Can I cover the vent leading to my crawlspace?
If that grate-covered hole is in a "common area" and up against a wall, you can bet that it was once a floor furnace. The combustion boxes on older gas floor furnaces would crack over time (decades) and become a carbon monoxide (CO) danger to inhabitants due to flue gas escaping into the home instead of going up and out the vent pipe. A utility inspector would red-tag (forbid the use of) the furnace when a new renter called for assistance with lighting the pilot light. Instead of replacing the unit, the landlord takes the easy way out and removes it, patching the wall above but with no easy way of repairing the hole in the floor. I have seen this exact scenario before.

To confirm, go up in the attic and see if there is an old vent pipe above the general area. If so, then go ahead and cover up that unneeded "ventilation" hole. It probably allows a musty smell in the house anyway. Do not disturb the old vent pipe if it appears to be something other than metal, it may be Transite pipe, which contains asbestos (a carcinogen).

Make sure there is really no functioning heating equipment down there before you cover it up (fire hazard). Your gas supply utility will send a technician to confirm for free if you tell them you have a safety concern.