I am getting a few evergreen questions with similar problems. My tree is an arborvitae that is turning brown on the south side. What is happening? It may be winterburn in evergreens.
The fancy term is winter desiccation. A lot of different plants suffered winter desiccation, including evergreens like arborvitae, boxwood and yew (maybe think twice about growing here), and white pine along with some spruces like Colorado Blue. Being evergreens, the trees and shrubs use water through their roots to keep the needles green and the plant alive. If the soil dries out during a thaw in the winter, or a dry fall going into the winter before soil freeze-up, a problem arises.
The leaves lose water faster than they can replace it, so the leaves/needles started to turn brown and die back. The south and west sides of the plant will show more injury because the sun’s intensity is stronger causing the needles to transpire.
For now, just watch the plant and see what happens. If it sends out new growth in the spring, then prune out the dead branches back to living tissue. If the plant is completely brown with no new growth, then you will need to remove it. Young plants are more at risk than older plants. Also, plants around the foundation of the home where water has trouble getting to the root are more prone to injury. Odds are they should come back.