wrap keeps temps up, and its for looks.
just stock up on the copper crush rings for oil filter changes
you can change the oil with the exhaust on.
I do this with my wrapped kerker.
Can't change th eoil with the carpy exhaust on...I'd suggest putting fresh oil in for the winter...don't let old/dirty oil sit over the season.
+1 on doing it as part of winter storage.
New oil (yup- both dino oil and synthetic), has rust inhibitors. In old oil those additives are 'used'.
Best bet is to follow the steps in the owners or service manual for winter storage.
(Changing the oil before putting it away for winter, is one of the steps)