Pat,

There are actually different species of dogwood that are native to Tennessee, but Cornus florida is the most common, so I will assume that that is the species you are concerned with. Since that species is particularly suseptible to anthracnose, pruning may be more of an issue than with more resistant species.

Dead, diseased, and rubbing branches should be removed at your earliest convenience, no matter the time of year. Additional pruning may be done in later winter or very early spring. Pruning in dryer times/conditions may be beneficial for reduction in anthracnose exposure. I've seen it recommended that you wait until warmer/drier weather (maybe late spring) to reduce the anthracnose disease pressure. Disinfecting of pruning tools, with spray Lysol or alcohol, and good garden sanitation practices may also help reduce disease exposure/spread.