Bagworms are an insect pest that can be reasonably well controlled with simple handpicking. Now is the time to look for and remove these insects, while they are still in the bag. Use hand pruners or scissors to snip off the bags as they are held quite tightly to branches and stems and pulling or yanking can damage the plants.
The bags are currently filled with eggs which ordinarily begin hatching in May. After the eggs hatch the small caterpillars crawl onto fresh foliage and begin to make their own bag which is quite tough and protective. Finding them is more of a challenge then, because they are small, and handpicking will be much more involved because there will be many more of them. Chemical control may be necessary at that point.
Junipers and arborvitae can be completely defoliated by a severe infestation which can occur with surprising rapidity. Many plants are host to bagworms. These include cedar, cypress, elm, fruit and nut trees, live oak, sycamore, wild cherry and willow among others.
Chemical controls are only effective when the caterpillars are still small. Spraying, best done in June, is non-effective during the rest of the year. However, handpicking is always in season.
Bagworm photo from Texas A&M