vinyl tiles in outdoor shed

We're converting an outdoor shed (cement pad, stuccoed exterior, shingled roof) into a playhouse. The floor is currently really dirty plywood. I was thinking of laying new plywood on top and installing the self-stick vinyl tiles. Reason being, it is cheap and I've found a pattern my kid loves. Potential problem I can see, is that it can get REALLY cold here in the winter time (down to -40 Celsius) and I am thinking the tiles might pop off this winter. The shed is not heated, but will have insulation with hardboard walls in the interior. They would have a summer with temps as high as +35 C before the cold weather shows up and the plywood would have proper prep done.
Anyone have any experience with self-stick vinyl tiles in an unheated building in a COLD winter? I am hoping to not have to resort to deck paint on the plywood.
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I would think you could do a single sheet of vinyl and have it stick Ok but the self stick ones I have always been leery of! One thing that may look really nice is to buy some waferboard and put a few coats of clear varnish on it!
Wayne

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