Despite my Canadian avatar, I live in Texas, so I can’t speak from practical experience about growing clematises in containers in the North. It is possible, however, to grow a clematis in a pot in a hot zone, and likely not that different in my native land.
It would seem that clems would not fit into my gardening style of naturalized settings with easy-care adapted and native plants. The fact that I can grow them should encourage you if you want to try them. My experience is in a warm southern climate, so the bloom times are generally better in the spring and fall.