According to an 1876 workshop book, horn mouldings were made by taking wafers of horn and compressing them together under heat. The horn becomes soft and the layers "weld" together, and it also takes the impression of any fine detail in the mould. The product can then be dyed any chosen colour and polished, or the wafers could be dyed before laminating.
You can see why the technique gave way to vulcanite (sulphur hardened rubber) and then synthetic plastic bakelite!