What type of door can be used for a utility room?
Based on your utility room and what is in there there needs to either be a certain amount of square feet or a certain amount of vented wall space.   This door would account for vented door/wall space.
If the door is needed for air intake - to meet minimum requirements - if you replaced it with a solid door you would have to add wall grills to that room.   This might defeat the purpose of trying to keep utility room air out of the basement.
The bigger issue probably isn't this door, it is why is your utility room that cold?    With working equipment - heater, water heater, whatever... and given your utility room is not conditioned (most aren't), it really shouldn't be much cooler than the rest of your house in the winter.   I would guess that the main issue you are having isn't that door, it is probably the air gaps and lack of insulation in the utility room.   You could probably fix your basement cold issue with $40 worth of insulation.