Will a lcd tv work ok in a unheated garage through the winter?

That depends. If you have enough money to purchase one, then a LCD can be in a garage. If you don't have the money, I would suggest getting a job (full time preferably) and then in about 3-4 months, you should be able to buy one. You probably can get the best deal at Walmart and probably won't have to wait that long. If you still can't get one, then ask yo momma!