A cavalryman is a soldier who fights on a horse. The group is the cavalry; one person in that group is a cavalryman. In old wars this was ordinary. In modern armies, units still called “cavalry” often ride in tanks or helicopters instead, but cavalryman still points back to the horse soldier. It is a plain, slightly old military word. Though actually, English also has cavalrywoman, but history books used cavalryman as the default for a long time, sometimes even for any rider in the unit.