I don't pretend to have read Cold Mountain, and it seems unlikely I'll view the movie. Kudos, nevertheless to publisher and producer for conveying to a mass audience the themes of Civil War desertion.
The best-known non-fiction work on this subject is probably The Free State of Jones. Jones County, Mississippi, attracted Rebel and Confederate deserters as well as runaway slaves who waged war on the local Home Guards and Confederate notables. Whether these counterrevolutionaries seized control of their county government and whether they actually seceded from Mississippi seems to be a controversy lasting to the present time.
The essential book on Civil War desertion was published in 1928 and is still available in a more recent paperback edition: Desertion During the Civil War is a short read, dense with numbers, anecdotes and implications.
A more recent work (A Higher Duty: Desertion among Georgia Troops during the Civil War) studies the circumstances of desertion and relates them to family straits. This author suggests that Sherman's march had a far greater effect on Georgian desertions than Grant's offensives.
There is, inevitably, the larger question of loyalty. Disloyalty in the Confederacy tours the peace socities, the unionist groups, as well as the levels of desertion from the Rebel cause.
The business of Civil War desertion is so vast and the readings available are so meager that one hopes Cold Mountain attains enough success to spark some new non-fiction pulishing on the subject.