When I purchased our new home 3 years ago,I initially thought I had moss growing on the trunk of my tree, but after thining out my trees to allow more sunlight through, the problem has gotten progressively worse. It covers the trunk and several main branches on two different trees. A few of our neighbor's trees also have this green substance on them. Could it be scales? I had scales on a new magnolia tree, which I successfully eradicated.
Sounds like Lichens more than scale. Lichens are a symbiotic relationship (mutually beneficial)between a fungus and an alga. They are not harmful. Worth taking a sample to the local garden center for them to have a look-seen none the less.