The history of the gaited horse is something that interestes me, here is what I have found in my reading and believe to be reasonably accurate.
Dr Deb Bennett's book 'The Conquerors: The Roots of New World Horsemanship" which covers the evolution of horsemanship, and horses, from domestication thru their (re)introduction by the Spanish into the western hemisphere. (If you want to know the deep roots of Vacquero/Californio horsemanship this book will trace it all out in excruciating detail.) Dr Deb uses the word "amble" to refer to all the "soft" gaits. The oldest known text on training horses, 3400 year old and written in cuneiform, is by the Assyrian trainer Kikkulis. This text covers the training of war horses (both chariot & mounted) and he speaks of using 3 gaits: walk, amble, gallop. The trot was to be discouraged because it didn't provide a stable platform for the warrior. " The horses in movies almost never amble, but Kikkulis's horses certainly did, and these facts hint that the modern reader may have to revise his or her mental picture of warfare in antiquity." (page 32) to continue "The road worn traveler, the weak, the obese, the effete, and the pompous are no warriors - and for their own reason these too have always preferred an ambler. Here is another surprise for the modern reader : throughout antiquity and right up until the early nineteenth century, no European of any means ever rode a trotting horse for preference. The equine most desired for war and for travel was one that would walk, amble, and gallop." (page 33) "It comes as a shock to modern students of sport dressage to learn that throughout the "classical period" of equitation all the better- quality riding horses were bred to amble as well as trot. The Renaissance manege not only called for but sought to increase the quality of the horse's ambling gaits" (page 112) As someone has already said, the riding of trotting horses became fashionable in Europe when better roads allowed people to travel by cart/carriage. To ride a trotting horse meant you were rich enough not to HAVE to ride. Luckily, this happened at about the same time as the Europeans were colonizing the western hemisphere -- so they sent the now unfashionable gaited horses to the colonies. If this had not happened thousands of years of breeding might have been lost forever. Our gaited horses are literally the result of about 4 thousand years of breeding for the best "riding" horses. Spanish jennets went to the south and west, they became the Fino, Peruvian, Cracker, & the orginnal american mustang. The hobbies and palfreys went to the east and north, the naragansett pacer and the candian pacers are examples of the early stock and from them come the TWH, Saddlebred, MFT, Mountain Pleasure, etc. The ambling (aka saddle) horse continued to be the preferred mount in the western hemisphere until the turn of the 20th century -- in South America & the Caribbean it still is. It was the horse of choice of US cavalry officers -- maybe the only thing that Generals Lee & Grant had in common was they rode gaited horses. During the time of the great cattle drives a trotting horse sold for around $4 dollars, an ambler went for 10 times that (>$50). If he could afford it, a cowboy rode a ambling (aka shuffler, single footer, saddler) horse. The great Native American war "ponies" were of Spanish jennet decent -- amblers all. Of course the Icelandic has a unique history, having been isolated from other breeds since about 900 AD, recent genetic research show the the Icelandic, Fjord & Shetland form a tight cluster, and together are the closet existing horses to the original cold blood horse of northern Europe. Kat