Hi: It sounds like you bought a frost free freezer as it has a fan. The fan will come on to circulate the air. It will not necessarly run continuosly. The noise is most likely coming from the fan. I sold Frigidaire freezers for years and they are noisy compared to a refridgerator. If you think it is louder than it was when you bought it, I would replace the circulating fan. Also look at the back wall for frost as it could be a bad defrost heater blocking it with ice. Most likely just the fan though. Since it's in a detached garage,and you won't have to put up with the noise inside your house, it could run a while before failing. The fact it's getting cold is a very good sign.Also as you asked 2'nd, a freezer is ok in an unheated garage. Don't put a refrigerator in there. Unless It is a Whirlpoll Gladiator that is designed for such applications. Use www.searspartsdirect.com
to find out where the fan is if you feel it is necessary to replace it. Its not a tough job if you are handy. Their shipping is expensive so you might want to buy it locally.