Spanish moss does not harm the tree. It takes its water and nutrients from the air, dew and rain. If I remember my high school biology class correctly, the oak is one of the very few trees on which spanish moss will grow. In fact, a dying oak will lose its moss, a sure sign that it is in trouble.
A bit of trivia learned in that same class, palm trees are not trees but belong to the grass family. Therefore there are 2 states that do not really have "state trees".
I will let you guess which.