bringing this up because I’m currently reading General Chamberlin’s Training Hunters, Jumpers and Hacks. The book is illustrated, and there is a photo of a TB stallion named High Line who is held up as an “excellent type of sire for hunters (eventers) and jumpers”. I looked him up on Pedigreequery, and he was definitely a Remount stallion. All of his get have the first name Reno, and some of the mares to whom he was bred have that prefix also.
Fort Reno in Oklahoma was one of the major Remount stations.
http://digital.library.okstate.edu/encyclopedia/entries/F/FO037.html
I found this 1911 army report on “the Remount Problem”. It’s fascinating. It gives a description of military related horse breeding in different European countries at the time, including Germany, France, the Austro Hungarian Empire, and Italy. Apparently GB did not make it a practice to breed cavalry horses, but imported them from its possessions and from the US. What it has to say about horses in the United states is very interesting, and it even has photos of the types of horse that the cavalry was buying for remounts at the time. It seems to have been just before WWI that the cavalry started breeding its own.
http://www.archive.org/stream/armyremountprobl00rommrich/armyremountprobl00rommrich_djvu.txt