Okay, I couldn’t find the Bruno Delgrange page which is a shame, because it mentioned thing I’ve never heard of before (standing in the stirrups to help the saddle settle on the horse’s back, etc), but this is what CWD says for care:
All new saddles have already been treated with ox-foot oil to optimize their first use. During the first week, daily use of CWD Conditioner is highly recommended to help waterproof the leather and enable the saddle to mould to the rider. Every day and throughout the saddle’s life, basic care is necessary. Daily care of your saddle is recommended to ensure that it lasts and remains in a good state. Firstly thoroughly clean it with CWD Saddle Soap using a damp cloth (provided with the CWD Saddle Soap) to keep the leather soft, pleasing to touch and efficient. Then take a dry cloth and wipe the entire surface. Then once a month apply a thin layer of CWD Conditioner with a cloth to feed, soften and deeply regenerate the leather.