Answer: While you could plant clematis in a container (the larger the better), since it is a perennial vine it will probably take it a few years to really look like much. Even when planted in the ground, the old saying is "first year they sleep, second year they creep, third year they leap". For this reason you might be happier with one of the annual flowering vines.
However, should you decide to plant the clematis in a container, it would do best in something large like a whiskey barrel. The larger container helps insulate the roots from summer heat and helps keep the soil moister longer -- important points because this plant likes a cool moist run run. You should probably also shade the sides of the container to try to reduce heat buildup.
For winter, you could bring the planter inside on a dolly, but it is very touchy to shelter hardy plants indoors in a garage or basement because the light and air circulation are so poor and watering is difficult to judge. If they are too dry they will die, but if kept too wet they will rot. For this reason it is probably better to leave it outdoors in a sheltered location out of winter wind and to insulate the barrel if possible. If you end up using a smaller container, the best thing to do would be to sink it in the ground or surround the pot with mulch to simulate the insulating power of roots planted in the soil.
Good luck with your vine!
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