Canadian Mounted Rifles was part of the designation of several mounted infantry units in Canada in the late 19th and early 20th centuries.
Canadian Mounted Rifles recruitment poster
Mounted infantry were infantry who rode horses instead of marching. The original dragoons were essentially mounted infantry. According to the 1911 Encyclopædia Britannica, "Mounted rifles are half cavalry, mounted infantry merely specially mobile infantry." Today, with motor vehicles having replaced horses for military transport, the motorized infantry are in some respects successors to mounted infantry.
Two Australian light horsemen in 1914