Answer: An unheated greenhouse may possibly be satisfactory, however it will possibly cause two concerns. The plants will do better with good air flow, since stagnant air in an enclosed space can encourage rotting problems especially under damp cool conditions. Next, the greenhouse can drastically overheat during a sunny day and practically cook the plants, then cools off quickly at night thus shocking the plants. For this reason you may have better success overwintering the mums outside if they are of a cold hardy variety. The difficulty with overwintering potted perennials is in protecting the roots from cold and in avoiding rotting of the roots or crowns due to trapping excess moisture. It is best to plant them in the ground, the next best being to set them in a sheltered location and insulate the pots with an ample quantity of mulch heaped around them. If you opt to overwinter them in the unheated greenhouse, try to keep the soil barely moist, use an automatic vent for colling during the day, and watch for fungal problems. I hope this gives you some ideas.
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