Hinton Hunt made two types of mounted figures:
the "horse attached" series, which were one piece castings (OPC) with the horse attached to the rider; these, I think, were the earlier figures
the "dismountable series", which had separate horses. There are fairly extennsive French and British ranges in this series, often of similar types available as OPC figures. The personality figures were dismountable, with some generic generals being OPCs.
On this blog labels starting with "type -" refer to mounted figures, while those starting with "pose -" are foot (infantry and artillery) figures.
You can search for mounted figures by nation, by type, or by series (dismountable or OPC)