There's a plant that's common in Florida, as well as other parts of the southeast and Texas, known as Spanish Moss.
It's not really moss, and it's native, not Spanish. Apparently the Spaniards and Frenchmen were trading jabs at each other by calling it "French Hair" and "Spanish Beard". Well the French version, taunting the Spanish, won out, with the slight modification to "moss" instead of "Beard".
Spanish Moss, Tillandsia usneoides, is a bromeliad, and epiphyte. This means it is not a parasite and does not steal from the tree on which it lives.
Deomossing for appearances only is generally not recommended. The effort to remove the moss can do more damage to the tree than it's worth.
A sick tree might allow too much Spanish Moss to grow. If that happens, moss thinning might be a good choice, but one should only remove enough to allow the tree to recover.