The short answer: it depends! Gardeners wrap their arborvitae in winter to avoid winter burn, which happens when the foliage dries out and dies from sun and wind exposure. Young arborvitaes planted in open areas in colder climates are most likely to suffer from winter burns. If this sounds like your plant, you might consider loosely wrapping it with tree wrap or burlap!
With that being said, not every arborvitae is susceptible to winter burn. If your arborvitae is in a sheltered location (protected from winds), has a mature root system (to access deep water reserves), or your area has mild winters (zones 7 & up), it will probably be fine without added protection.