All evergreens including arborvitae are alive all year round and can be impacted by a strong seasonal change in the weather pattern, be it cold, drought, or unseasonable rainfall. A plant only one year old is not likely established in your yard yet and has a limited root system. Whether balled and burlapped or container grown, the roots need 2 or 3 years to develop in your soil. If he branches/twigs where the needles have browned are still pliable, the branch is still alive and can regenerate new needles. You need to monitor the soil moisture where the roots currently are, essentially where the root ball is or in the diameter area of the growing container. If there is a warranty involved, please inform the retailer and follow their recommendations.