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my softtop was down for years as I ran a hardtop most of the time, it never suffered from being down, and any wrinkles disappear once up, so you can do whatever you like with yours. The top is not the issue in cold weather it is the plastic window on early ap1's that can suffer damage in cold weather. If your top has a plastic window I would not move it in winter, if you have a glass window do as you like. The softop material is not adversely affected by cold temps.
Similar experience here. My HT has been on since 2006 amd rarely removed. Last Oct I put the softtop back up for a day and top was still good.
I wish I had a garage because my top is in great shape and id like to keep it that way all I have is a cover. But I guess it's better than nothing. Also I came out one day to 5 bird shits on the roof and said helllll no!
I'm persuaded the top can be stored down even in the cold without damage.
Still, I will leave mine up just to give the cover support during storage. Once the car comes out of storage, my top is down almost all the time.
Both in the garage during the warm months and in the storage shed during Nov-March, mine is top up but not latched. It keeps the material from developing creases/weak points without keeping it stretched tight during below freezing temps.