Depending on the tree's age and other conditions, brown leaves on a cedar may simply signify the natural aging process according to North Dakota State University's horticulture department. In more mature cedar trees, brown leaves may be a sign of trouble.
If the cedar in question is around 2 years old and is turning color in colder months, the browning of the leaves may be explained by the natural maturation process that is unique to cedar trees. This is the only normal time that this evergreen tree should show signs of browning. If this is not the case and the tree is older, much younger, or browning in spring or summer, it could have a root rot issue. If the tree is very young and its branches and trunk are turning brown, this is also part of the normal maturation process. As cedar saplings grow, their branches, twigs and trunks turn from green, gray or reddish to brown.