Is moss on my oak tree harmful, and how can I keep it healthy?

It sounds like Spanish moss (ball moss and resurrection fern don't fit the description "draping"). Spanish moss (Tillandsia usneoides) is an epiphyte, not a parasite. Epiphytes derive all their nutrient and moisture needs from the air and from rainfall, not from the host tree. Question is, is it harming the tree? While Spanish moss may not directly harm the tree, an unusually high population tends to be an indicator that the tree is under distress or in decline. When a tree is under stress or in decline, every opportunist in town gravitates to that tree, including Spanish moss. Spanish moss is said to like full sun or partial shade, so as a tree's leaf population decreases due to various stress factors, the Spanish moss population tends to increase. There are other stress factors, such as poor soil nutrition, root rot, leaf disease, inappropriate irrigation schedule, decay, etc. that can be investigated as well.