These "bags" are probably bagworms. Bagworms hatch in mid to late spring and the tiny caterpillars begin feeding on foliage of both deciduous and evergreen plants. Bagworms fashion a small bag around their bodies made from silk and the foliage it is feeding on. It drags this bag with it as it feeds. When disturbed, the caterpillar withdraws into the bag. Bagworms feed on many different plants, but they prefer arborvitae and red cedar. They can cause extensive damage to evergreens because the foliage is not replaced. If you've had problems with bagworms in the past and/or have valuable evergreens, it may be worth checking for the pests each season. If only a few bagworms are present on a plant, simply hand pick them and drop into a jar of soapy water. If numerous, the plant can be treated with a labeled insecticide. Contact your local Extension office for chemical recommendations.

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