There isn't necessarily any need for a vapor barrier/vapor retarder between the floor joists and subfloor of a room over a garage. And adding a vapor barrier/vapor retarder is not going to help your cold room get any warmer. You should have at least R-30 insulation in the floor depending on your location. (Please tell us what state and county in which you reside) An AIR barrier will help in your case. 30-40% of energy loss in a home can be attributed to air infiltration/exfiltration. To answer helpfully, however, we need to know where you live...
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