Assuming that you’re following the recommended oil change intervals, there is no reason to put new motor oil into your Corvette right before storage. This is especially true with Mobil 1, which, as you know, was factory fill in your Corvette. Because Mobil 1 generally has a longer "shelf life" than conventional motor oils – i.e., it will not deteriorate as quickly in an engine that is not being run for months – Mobil 1 will retain much of its lubricating properties over the months of winter storage. When you first start up your Corvette’s engine in the spring, a thin film of Mobil 1 will still exist on many engine parts, and Mobil 1 will flow quickly into the oil galleries and onto lubricated engine parts, helping to protect your engine. It is at this point, when you plan on driving your vehicle again, that you should change the oil to fresh Mobil 1 and a new oil filter.