This is a horticulture question, but I can tell you the answer. The worms you described are Bag Worms, named because of the sacks they make and hang in. They can be harmful to a tree because they feed off of it, robbing a tree of the nutrients it needs to grow. They can especially hurt a young tree with a big enough infestation. Ideally, the sacks should be pulled off, collected, and burned instead of just dropping them on the ground. Bagworms often spread to near by trees, so chances are even though you notice them on one tree, you will see them on others as well. Below is the information from Lawn and Garden solutions on bagworms via our urban website www.solutions.uiuc.edu/
"Bagworms feed mainly on evergreens, though they can be found on many deciduous trees and shrubs, forming a "pine cone-like" cocoon to live in. Bagworms overwinter as eggs in old "bags" that hang on trees, and hatch in June. New bagworm larva move throughout the plant and feed on leaves and needles. Bagworms pupate in the fall; males leave their bags and mate with females who stay in the bag. The female lays here eggs in the bag and dies.
"Bags" are difficult to penetrate with sprays, though easier in early spring than later in the year. Handpicking may be the best means to remove the bagworms, especially in the early spring before eggs hatch.
Control sprays should begin around the first of June as eggs hatch and form new bags. Several applications may have to be made throughout the month. Make sure to read and follow all labeled directions."