Answer: It can be difficult to grow plants in containers outdoors year round because the roots are not as well insulated as they would be if planted in the ground. If you want to use trees or shrubs, you will need to use very large containers (half whiskey barrel size or larger for example) to provide both insulation and adequate root space for healthy growth. You should check and see if your deck is strong enough to hold that type of weight -- a large container of damp soil can easily weight hundreds of pounds.
It makes a difference whether the half day of sun is in the morning or the afternoon. Afternoon-only sun is very hot; plants dry out faster and are more stressed as a result; it can also cause extra winter stress on plants. In contrast, morning sun is milder and gentler and easier on container plants. Wind is another consideration. If your deck is windy, especially in the winter, then you will be more limited in your plant choices -- I would not recommend evergreens for a windy spot for instance.
Here are some suggestions. You could experiment with growing smaller crabapple trees, lilacs, forsythia or privet in your large containers year round. Understand that you may need to replace them every year. Another option would be to grow young hardy plants in the containers all summer and then plant them in your yard in the fall to become part of your permanent landscape. Or, you could grow large house plants such as palms or ficus trees and bring them indoors for the winter. Or you could grow tender plants such as tree roses or figs in the containers and bring them into a sheltered location such as an unheated garage for the winter. Or you could plant annual vines such as morning glories or moonflowers in the containers and replant them each spring. Or, you could plant a hardy vine in the ground below the deck and train it up a trellis as high as you need it.
I hope this gives you some ideas.
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