This is actually a lichen rather than a moss, and nope, it's not harmful. It's just growing on the bark of the tree, rather than being any kind of parasite.

Patrick Alexander

As Patrick said, no, but if they cover the branches and the leaves of the tree look smaller than normal, discolored, etc. then you may have a disease problem. Lichens will often colonize diseased bark and while they are not the specific cause of the problem, they can be an indicator there is a problem. This however not always the case. If your trees look happy, then there probably is no problem. I've seen overgrowth of lichens on diseased azaleas and crape myrtles, but not much else.

The common name for your lichen is Ball Moss, which is pretty unsightly as it thrives in declining trees and shrubs. Pay close attention to the overall health of your plants, try to invigorate them by pruning out dead branches, by mulching, and by some conservative fertilization in the Spring.

If I had a heavy infestation of Ball Moss (a relative to Spanish Moss...also not a moss, but a lichen), I'd remove them by hand or by clippers. Not because they are causing serious problems for the plant but because they are so darned big and homely. They are a real problem in nurseries.

Sorry rhizo1 that ain't ball moss, but a lichen. I've never seen problems with ball moss (except for its unsightliness), but occasionally spanish moss will overwhelm a smaller tree.