Mine all go "dormant". However, newly rooted cuttings and small trees seem to hang on to some of their leaves longer, even through the winter here. Some trees keep some leaves all winter, and while they might not be fully dormant, they are also not active. Grafting this Spring on small plants with leaves still on (so not "dormant") was not as successful as it would have been if done when they are actively growing, so the presence of leaves was a seeming indication of non-dormancy, but the plants were still nearly or practically dormant.
Many trees were not fully dormant, and many definitely still had green wood at the end of January 2010.
As little dormancy as my trees get, they seem to be fine with it. I think most literature would support the idea of some minimal amount of dormancy being good for the tree, even if not required in the way an Apple or other fruit requires chill hours to fruit successfully.