Unless you have a radical valvetrain, there's no reason to use "boutique" oils.
Change oil just before you put the car up for winter storage - you want fresh, clean oil sitting in it all winter, not last season's dirty oil.
X2 to both things John said...
The old oil has all those "nasty deposits" in it, so you would not want it to sit all winter. Even if you haven't driven it that much, you really don't want old oil to sit idle that long.
On all my classic cars, I have an oil change and lube done before I store them. Also, I fill the gas tank and add Sta-bil to keep the moisture down in the tank. And... I keep an eye on humidity and minimum temperature.