It seems to me this question came up on the MR forums a year or two back. Someone who apparently had good knowledge of the issue said that on some trains crossing from north to south, the seating would be pre-arranged so people didn't have to move - a black passenger taking say the IC from Chicago to Mississippi would be seated in a 'colored only' car at the start of the trip so they didn't have to move. Not sure if that's correct, but it would make sense. Apparently dining cars weren't segregated until they crossed into a southern state, then a divider would be put up or something to separate the races.
"Colored" cars were often very old, I know a number of 19th century passenger cars that are now in museums were only preserved because they were used for black passengers into the 1940's-50's in every day service.
