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An easy way to overwinter some plants is to grow them in containers year-round and use them as houseplants or on the sun porch during winter. Slow-growing woody plants such as lavender, rosemary, and tarragon make the transition from outdoor plant to houseplant and back very successfully and can thrive for many years.
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You can hold many types of nonhardy plants, often called tender perennials, indoors over winter. Cutting back, digging up, and potting plants growing in the garden is one option for overwintering, but this may cause transplant shock, especially if the plants are large. An easier way to save tender perennials is to take and root cuttings, and then keep the cuttings indoors over winter. Many summer bedding plants, including impatiens, begonias, geraniums, and coleus can be overwintered this way. Rooted cuttings take up less space indoors than entire plants, and there is less chance of inadvertently overwintering diseases or insect pests. Take cuttings from your overwintering plants in late winter to propagate more transplants to move outdoors once the weather warms. To keep them from getting leggy as winter progresses, pinch them or keep them under plant lights.
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The fleshy roots of cannas, dahlias, and even four o'clocks (Mirabilis jalapa), along with tender bulbs like caladiums (Caladium spp.) and tuberous begonias (Begonia spp.) can be dug and stored over winter.
Geraniums (Pelargonium spp.) and other tender plants can be overwintered two ways. Bring them indoors as described above, or force them into dormancy. Forcing dormancy is useful if you're short on space for houseplants or want to save time and effort on winter care. Put the plant, either potted or with newspaper wrapped around its root ball, in a cool (not below 40°F), preferably dark place for winter. Allow the soil to dry somewhat but not completely; check every few weeks and water sparingly if needed. In spring, replant outside after danger of frost is past or place in a warm, well-lit place and resume watering.
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Many tender perennials go dormant by themselves, but need protection. Cover them with a thick layer of mulch, or dig and move to a cold frame or cool basement. Overwinter container plants outdoors by packing them in the center of large boxes packed full of leaves. Wrap shrubs and vines that need winter protection, or bury them in trenches.