Good idea. Carefull though, if it gets really cold in your area the cooler will eventually equalize with the garage temps. But if the temps fluctuate enough into the warmer range the cooler would probably be a good way to keep things warmer than the ambient cold spike.
I keep my garage door down all the time and the entire garage is fully insulated. the only time it gets below freezing in there is when the temps are in the -0 range. I have a few items I keep inside, usually the stuff I spend the big$$ on. I just keep them in the toolbox I keep my PC in.