ONLY max performance tires, generally 100wt (racing/track) or 200wt (track) are problematic when it comes to storing and driving 24hrs after being exposed to very low temperatures.
You basically need to allow tire to go back naturally to its properties.
Summer tires, performance like Micheling PS4S etc. are fine storing. I store my Yokohama Advan V601 that I track in a shed outside.
That being said, if you want all year around tire, Michelin Pilot AS4 or DWS06+ are best bet. Unlike your Pilot AS3+, mine on Tiguan are super quiet going 4th year.
I have DWS06+ on BMW for May-November and they are excellent. However, they are bit softer and not having steering feedback on par Michelin. I run 39/41psi to compensate. They are EXCELLENT in rain. Hydroplaning resistance is excellent, but braking and handling traction in rain is impressive.