From Evergreen Gardenworks
"Growing mume is problematic for many people including us. After a long hiatus, we are attempting to grow it again. The basic problem is that they are very susceptible to spring freezes. Their early flowering means that they are active very early in the spring. Any hard freeze after flowering begins induces small freeze damage cracks along the branches that are invaded by spring fungal diseases. Often these diseases are fatal to the tree, but if not fatal, large branches can be lost. We now have a large greenhouse that will allow us to overwinter a few stock plants and hopefully a yearly supply of smaller plants for sale. Mume will perform best in areas that are mild in winter, and that once warm, stay warm without spring frost danger. Dry weather in spring also helps with the control of fungal diseases. Some disease control is possible with fungicides, especially fixed copper, but repeated applications will be necessary. Fortunately, mume grow quite well in containers with frequent repotting and this allows them to be moved into a protected area temporarily in spring. An overwintering cold greenhouse is ideal for them, such as a covered porch or traditional greenhouse."
With that said, I have a few and I'm in your zone. I have some in the ground that I am growing out and one in a pot. Once i notice buds on the one in the pot getting ready to open i protect it from freezes.