Admittedly I haven't done a proper survey, but the impression I get is that most posters here think that the planter class will try to maintain the world of 1859, fail, and get overthrown somehow.
One thing I'm not seeing acknowledged much is that in a CSA victory, it's not like this would be costless, unless it ended after Bull Run, in terms of the planters. Most were ruined by the war itself, the ones left by the postwar economic malaise and epidemics of the 1880s, or from collapsed demand. A southern victory in 1864 means that the invasion of the Delta and Lower Mississippi still happened, as did coastal incursions across the South. This was ruinous for planters, immediately. Many became internal refugees and lost all wealth that was not liquid. The planters also, despite what the stereotype was about a rich mans war and a poor man's fight, etc, served the CSA in disproportionate numbers at all ranks but especially as junior officers, which suffered horrific casualties in the war in battle. Gallagher's book demonstrates this but it's important to note what chaos this caused for inheritance, land claims, and estate consolidation. A lot of property was lost from war related deaths and split among relatives who couldn't maintain it with their existing capital pool.
The planters were not a monolith either. The biggest ones were mostly ex-Whigs who didn't favor secession, at least at first, until a binary choice was put to them. Most of the rank and file fire eaters and secession friendly elites were fundamentally second rank in the social sphere - ambitious lawyers and politicians, and smaller planters who were being squeezed by high slave prices in the 1850s and difficult export markets.
I don't think they'd retain much power for long in the CSA, which would likely develop a political elite tied close to the army, an institution with more varied social backgrounds at the top