The winter care of mandevillas like many tropicals can be one of two methods. If you have the space, they can be brought indoors and grown as a houseplant. Place the pot in a sunny location. A greenhouse is ideal. Water about once a week. Trim as needed to maintain the desired size. Mandevillas will not bloom through the winter due to the shorter days unless they receive supplemental lighting. With this method don't be alarmed if the mandevilla like many tropicals insist on going dormant and lose their leaves. They often look dreadful during the winter.
The other method is the "just don't die" method. Dig the mandevilla from the garden or bring in the container before temperatures get below 60 degrees F. Trim the plant back to about 8-10 inches. Wash plant thoroughly. Drench container soils with water to encourage any critters like ants and sowbugs to vacate. Store the plant in a cool dark basement, garage or crawlspace. Anywhere where the temperatures stay about 55-60 degrees is adequate. Do not fertilize during the winter.
Keep the soil on the dry side, but do not let it dry out completely. In the early spring the plant will form shoots. Move it to a sunny spot indoors and pinch shoots periodically to form a bushier, more floriferous vine. Before setting outside in late May or early June, repot and apply a water-soluble fertilizer. Do not set outside until all chances of frost have passed and temperatures stay above 60 degrees F. good luck,