Actually the Empress was not the first one to scratch her name into the pane. This is a much older tradition in the Hessian Family and to be found in other residences as well - such as Kranichstein, Braunshardt , Fürstenlager and Romrod.
Even in the 18th century the Landgraves of Hesse Darmstadt and their relations used to write on the wooden panels near to the windows in the Grand Drawingroom at Wolfsgarten. The eldest inscription I saw dates back from 1772.
When Ludwig IV. decided to revive the "sleeping beauty" in 1881 he and his children began to scratch their names into the windows. One finds "Ludwig IV 1881" "Ella 1881" "Elisabeth PC" "Alix" "Ernst". The signatures include Queen Elizabeth, Prince Philip and their children, Adenauer, Britten, Mick Jagger, Menuhin etc