Actually, the Battle of the Crater (July 30, 1864) at Petersburg, Virginia was what was portrayed at the beginning of 'Cold Mountain.' I don't think Vickburg as been done yet, except in the old 1980s miniseries "The Blue and the Grey."
Not meaning to make an off topic tangent, but I would love to see a movie done about the Vicksburg campaign. US Grant really showed his genius and tenacity during that one.
The Crater, then and now.