Green moss can be unsightly and slimy, but that's no reason to pull out the toxic chemical spray. The herbicide may adversely affect surrounding greenery, and the green moss will likely return over time. The best way to get rid of green moss on tree trunks and fences is to physically remove it and then discourage its return by drying out the area.
Turn the hose on and place your thumb partially over the opening so that the water comes out in a forceful spray. Then spray the green moss until it is forced off of the tree trunk and fence.
Fill a bucket with warm water and 1/2 cup of vinegar per gallon of water. Dip a scrub brush in the solution and scrub off any remaining green moss from the tree trunk and fence.
Spray the area with the hose once again.
Increase the light and air circulation. Moss thrives in dark moist conditions. If possible, trim back the branches of surrounding trees to allow more sunlight in. If an adjacent building is preventing the area from enjoying more sunlight, simply re-treat the area as soon as the moss crops up again.