Will freezing a bottle of vermouth change it's quality, life length or properties?
I've frozen bottles of vermouth many times. There is no issue with just letting it thaw out in the normal way. In fact you can wait until it's partly thawed, give it a good shake, and hey presto, vermouth slushy, which goes in some cocktails rather well. Fortified wines do slowly oxidise on exposure to the atmosphere, but this is greatly slowed by the alcohol content. Historically this was one the principle reasons for fortifying wines - so that they store better and last longer.