When a very senior Head Butler wore white tie, the Downton version is correct. It is, however, right that the long tie also existed, but it was generally considered, such an abomination, that at least the bigger houses refrained.
The English aristocracy favoured dressing their servants slightly incorrectly, in order for them not to be taken for a gentlemen guest, consequently for instance a Butlers informal day attire (in certain periods of time), would consist of a stroller and wing collared shirt with a (long) black tie.The formal day uniform would be morning suit/wing collar and also long black tie!
Do you mean red haired? - then the answer is no, it's brown/white - if you mean red faced, that's part of being an old fart! That is an art installation in the park of the Odrupgaard Art Museum where the Van Gogh/Gaugain/Bernard exhibition is presently showing.