The issue you are having seems to be a bad lcd. Im guessing the cold may have had something to do with it or the change in temperature when turning on the device caused a tiny bit of moisture to short something. This is why it's best to keep electronics inside during cold and hot days because they can either short or overheat. I don't know off the top of my head what the s2 and s3 lcd connectors look like. I'd assume they are different, so I wouldn't trust it unless you are confident the connector is the same.