The term 'soldier on horseback' can be summarized by two crossword solutions: LANCER (6 letters) and CAVALRYMAN (10 letters). A LANCER is a soldier who fights with a lance, a long spear-like weapon. Historically, lancers were used in mounted warfare, often as part of a cavalry unit. A CAVALRYMAN is a soldier who fights on horseback, usually as part of a cavalry unit. Historically, cavalry units were used to charge enemy lines and break through defenses.