Fuzzy Green Growths on Rose

My rose is covered with these fuzzy green growths. The plant seems to be doing fine but it looks like some kind of moss or another plant has sprouted out of the stems.

It sounds like mossy rose gall is the problem. Wasplike insects bore into the rose stems and lay their eggs. The eggs hatch into worm-like larvae. Their presence in the stem causes the plant to form the swelling known as a gall. During the growing season it is often covered with green mossy-like growth. There are no chemicals that control this pest. Continue to prune out and destroy the galls as they are found. Do a thorough exam in fall and remove any galls found. This eliminated the spring hatch and can help reduce next year's population. Fortunately weather and natural predators usually keep this pest in line. I have noticed more problems with this pest in the last few years so we may be on an upward climb in their population cycle. Typically an insect population increases over several years. As the pest population reaches peak numbers its natural predators or a disease moves in and reduces the population. So continue pruning and be patient, nature may soon step in to lend a hand.