Corbet what's the dimensions of the window? I bet we could come up with a material & thickness recommendation for you... you would want to leave some slop in the frame to allow for thermal expansion/contraction, also you wouldn't any fasteners drilled through it- how far away from the current window could you theoretically install this new "storm" window? That will dictate how much deflection you can have.
But heck you can make anything from an airplane window to an aquarium out of plastic, a little snow shouldn't be a problem.
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