The plants attached to your tree are ball mosses. Despite their common names, Spanish moss (Tillandsia usneoides) and ball moss (Tillandsia recurvata) are not mosses, but members of the Bromeliad family. Ball moss is a small, tufted, gray-green plant. Both prefer high light and will therefore thrive on weak or dead trees with few leaves.
Most people assume since they are found on dead trees the ball moss is causing the trees to die. Some false information has been spread about Spanish moss and ball moss being a parasite, but this is not true. I have also seen them attached to healthy trees too and even telephone wire. In the case of declining trees, there are other issues and more common causes such as piling soil on top of tree roots, planting grass too close to the trunk, heaping mulch up to the trunk in layers more than 2-3 inches thick – all of which can compact the soil removing important oxygen from the root area. Limb breakage is often attributed to the weight of Spanish or ball moss, but in fact, moss contributes an insignificant amount of weight and is almost never a factor in broken branches. The branch was likely weak or damaged and would have failed on its own.
Bottom line: plant damage resulting from Spanish or ball moss is uncommon, and removal is expensive. Consult with an International Society of Arboriculture (ISA) Certified Arborist before attempting to remove moss. These professionals can assess the health and structure of your tree(s) and determine if moss removal is justified especially if it is high in the canopy. If the ball moss is low enough in the canopy, you can remove it by hand.
For more complete information on Spanish and ball moss, read the University of Florida publication titled: “Spanish Moss, Ball Moss, and Lichens – Harmless Epiphytes” by Joe Sewards and Sydney Park Brown. https://edis.ifas.ufl.edu/ep485