I disagree that a steel-vinegar solution makes red oak black:
I've shown this before, but this is one example of what you can expect from a ferrous sulfate solution on red oak. (Note - different woods respond differently. The quoin was made out of a different wood, and didn't react much to the treatment. A paint stirrer and a few other pieces of scrap wood I tried (of unknown species) all had different reactions. This acid reacts with tannins, and only woods with high tannin content will have significant reactions.)
This color was created by dissolving some 0000 steel wool in a cup of vinegar, then rubbing it on with a rag. Initially, it turned grayish purple, but after neutralizing the acid with a baking soda-water solution, I applied some linseed oil, which left it a nice distressed color. Hand forging the trunnion hardware added an aged look, as does pulling it around on gravel, firing it, and leaving it out in the rain during once in a while.
I do agree that an authentic aging would require painting, then wearing off the paint and ditressing the paint finish, but I also like to see the grain of a nice wood. I disagree, though, that you should start with old wood. You should build the carriage as if it was being built for the first time, ideally using old methods (like the scrapers and other hand tools). It should be built to the standard of the originals, then worn to the level of aging desired. Many of the originals were made from new wood, repurposed wood, or a mixture of the two. I think having a mix would be interesting, especially if you chose to go for the peeling/worn paint finish. If not doing the paint finish, I'd stick to new, then you can age to whatever degree you want.
Whatever you want to try, attempt it (in the same sequence) on a scrap piece from the same board you want to use.