If your arborvitae turns brown, it could, depending on the time of year, be due to winter burn. So how do you prevent arborvitae leaves from turning brown? And if browning does occur during the cold weather months, what action, if any, should you take in spring?
If your arborvitae turns brown over the course of the winter or early spring, the cause may be winter burn. The combination of wind, sun and lack of available water in winter can cause arborvitae foliage to turn brown, due to dessication.
Regardless of the type of arborvitae you plant, you're best bet for avoiding winter burn is to wrap the arborvitae in burlap. Placement also helps prevent browning: avoid planting arborvitae on the south side of a wall or in an area exposed to high winds. Finally, many recommend easing up some on watering arborvitae in September to encourage hardening off, then maintaining adequate irrigation from October until whenever the ground freezes in your area.
Arborvitae branches whose foliage turns brown (entirely) due to winter burn may not come back, but there's no sense in being hasty about pruning (you never know!), so I'd hold off on pruning until well into the spring or even summer. Only time will tell as to whether your arborvitae branches will recover from winter burn; there's not much you can do to reverse the damage that results in brown foliage. Instead, direct your efforts at preventing winter damage in the future (see above). If green growth does, eventually, re-emerge on a branch damaged by winter burn, prune the branch back as far as that greenery; but if the arborvitae branch never shakes the "brown look," just prune if off entirely.
For browning on arborvitae in summer, consult my FAQ on leaves turning brown on Emerald cedars.