You should really apply a sealer or sealer/primer combo to new pine. And shellac any sap spots or knots.
I think like most painters I hate hearing about using adhesives on any painted surfaces and have spent more time than most trying to deal with such things in the gallery world.
Have you looked into the interior storm windows? They snap fit in place from the inside and work out to be cheaper than the shrinkwrap plastic in the long run since you re-use them each season. Here is a link to one company I have used. There are others. The nice thing with interior storms is you don't have to be crawling around your house on an extension ladder. This was an issue with clients that owned tall Victorians. Of course you have to store them off season.
Of course there might be a problem with something patio door side.
You might think about stapling velcro buttons and stretching the shrinkwrap to them. Staple them in place and don't use the adhesive. Staple holes are easy to patch.
You could get really tricky and recess screws you would never see again. Use the tiny super magnets to hold the plastic to them.