Answer: Mandevilla is a tropical plant and will not survive winter outdoors. There are two methods for trying to overwinter it without a greenhouse. One is to keep it in a cool, dark place such as a basement in the 45 degree range and barely water it -- just enough to keep the soil from going bone dry. (Whether or not you will need to water will depend on the storage temperature and on the soil mix you have used.) This treatment is intended to make the plant go dormant. In my experience it worked best when we left them outdoors as late in the fall as possible and the older larger plants in larger pot handled this "abuse" better than younger smaller plants, but they tended to try to come out of dormancy in February so the problem was finding a bright sunny spot to keep it in (as described below) until it could go back outside.
The second method is to treat it like a houseplant and keep it growing all winter -- provide as much sun as possible (full sun is what is needed) but water/feed less and less as the days grow shorter and the plant growth slows down. This plant will often lose its leaves when brought indoors and look pretty ugly for at least a while until it acclimates to the reduced light levels and drier inside air. You can try to minimize this by moving it gradually indoors (just as you would gradually move it out in the spring) and by maintaining humidity and keeping it away from drafts.
Good luck with your plants!
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