When I had kayaks I got cockpit covers for them.. like a skirt but no way in. Like you, I had to store them outside. I put the kayaks under a deck and forgot about them until next spring. To prep for winter I washed out the inside, made sure the hatches were empty, made sure they were completely dry, covered the cockpits, and bob's your uncle. Now I have canoes. I store them upside down on saw horses. No prep, no cover. What you should NOT do is to let any kind of tarp rest directly onto a fiberglass, kevlar, gel-coated boat for long periods when there is a lot of sunshine. Boats can easily de-laminate from that method.

No mice ever went into my cockpit covers but during the same periods they managed to visit inside the house more often than I'd like.