I googled the origin of "clothes horse" and didn't find an exact explanation of where the term originated. But it does say that the term used to mean a wooden frame used for drying or airing out clothing. Maybe it stood on four legs and sort of resembled a horse. Other useful items were also called horses, such as sawhorse and iron horse (locomotive). A person who works very hard can be called a workhorse. But how the term got translated into somebody who is often elegantly dressed remains obscure.