Q. Are there any small trees that grow in containers that could be left on the patio year round?
This is a frequently asked question so I am repeating the answer already found in this database:
Ray Rogers, author of the book Pots in the Garden ; expert design and planting techniques provides a very good list of suitable trees and shrubs ranging from Japanese maples (Acer palmatum ) to color-twig dogwoods such as Cornus sanguinea to Honeybush (Melanthus major) to various junipers.
The PHS McLean Library has both the print and eBook version of this book. Attached is a plant list from Pots in the Garden.