I take it the question here is my proposition that in the Early Middle Ages, the horse was the preserve of an élite used for mounted warfare and high-end travel, but that by the High Middle Ages, horses had become ubiquitous.  The question does not relate to a query on whether all mounted fighters were part of a social élite.

My proposition is really based on two observations:

1. In the Early Middle Ages, there is practically no evidence for horses in a draught function, i.e. for wagons or ploughs.  To the extent heavy draught animals were used, it was oxen.  Horses were used as pack animals, of course, amply documented in Carolingian times.  But gradually, as the technology accumulates, horse-adapted rigging appears.  The elements here are pivoting front axle, whipple-tree, shoulder-collar …  much has been made of the shoulder-collar as a major step; I think that is over-emphasised, it was more of an incremental improvement rather than a step-change.  It is the combination of these developments – along with an improvement in roads – that interacted to make the horse more relevant.
2. The other factor is a retrospective one – in the Carolingian sources, the horse, when mentioned, is an elite animal.  By the 12th C, we begin to have manorial records, and there, we find a wide variety of horse functions.  So somehow and at some point, there must have been a transition from the Carolingian status and prevalence of the horse to 12th C prevalence of the horse.  Since this transition is mirrored in the development of rigging and wagon technology, I submit that the story is consistent.

Another supporting element is agricultural archaeology; the 9th C saw the transition from the two field rotation to the three field rotation.  That immediately boosted agricultural output by 1/6.  But the story is more complicated.  With the two-field-rotation, farmers were forced to focus on the essential crops, and that was bread grains (wheat and barley).  With the three field rotation, it became possible to plant a wider variety of crops, and that benefited oats (and other crops – our research tends to focus on grains, though beans and pulses (i.e. lentils) were probably more important than is appreciated); and bear in mind that this is contemporaneous with the development of the heavy, mould-board plough, which now opens up the heavier soils of northern Europe for intense cultivation.  Oats do not have a high yield, but they are more tolerant of cold, wet and dark.  It has been established that horses are able to extract 80% of the energy from oats; for other grains, the efficiency is 40% or less (from memory).  Of course, oats are perfectly fit for human consumption, delicious in fact, but if there is a God, He designed oats as food for horses.

As a further aside, the increase in agricultural production flexibility also benefited cash crops such as barley (for brewing) or linen and hemp.  All of these industries too take off in the High Middle Ages.
I have not focussed on the iconography.  There may be more support there. So on balance, there is no(t much) direct evidence, but clear  status quo ante and status post quem, and multiple consistent story lines and developments in between.

The short answer is that I am unaware of any direct connections between Grisone and Duarte. According to the Forgeng translation of Duarte, there have only ever been two copies: the original manuscript (now lost) and a copy made for Duart’s wife Eleanor (Paris Bibliothéque Nationale MS Portuguaise 5). The copy was in Naples in the late 1400s, but may have been transported to France after Charles VIII conquered Naples in 1495, or possibly sold to Louis XII of France in the early 16th century. After 1544 it was listed in inventories in the French Royal Library.

Given that Grisone was born in 1507, it seems unlikely the book was still in Naples when he was alive. The text was referenced a few times by other authors (without any details), so it is certainly possible that there are lost works that discuss it in detail. However, if Grisone was aware of Duarte’s text, it does not appear to have had much influence on his own work, as the foci of the two books is quite different.
Having said that – new information is always coming to light, and I would be happy to be disproven!
@Jennifer JobstDoes de la Broue mean you have no bend in the horse when riding a traversale?

Correct, de la Broue explicitly says NOT to bend the horse in a “bias” movement. “Par la ligne de la lettre A, on peut iuger de plain droit & naturel auquel le cheual doit estre maintenu sans luy laisser plier le corps ny le col: par celle du B est representé la piste que doit tenir en ceste premiere reigle le pied de deuant, qui deuance & cheualle: la ligne du C signifie la piste du pied de derriere & du costé de l’obeyssance, comme il est aussi figuré par la peinture des fers.” [By the line of the letter A, it is legitimate and natural to which the horse must be kept without letting him bend the body or the neck…]

This is the diagram associated with these instructions – you can see the letters he calls out in the text:

The reading list can be found here, under the 16th and 17th century headings: https://pieceofheaven1951.blogspot.com/p/research-bibliography.html

Yes, if you watch videos of horse trainer’s Monty Roberts join-up technique (https://www.youtube.com/watch?v=vYtTz9GtAT4), you see that submissive postures in horses involve dropping the head, licking and chewing. Imitation of this body language would have some communication meaning and pscyhological effect on horses just like squaring your shoulders and facing them directly will scare them away while turning to the side to approach them with your shoulder to them and not the whole front of your body is considered less aggressive behavior by them and more welcome. There’s less pressure with the side on approach than the full on. So location of the body as higher or lower or of the head as higher or lower might make the horse himself consider the other person as submissive. It might be easier to get an already somewhat aggressive animal like a stallion trained to step on people or that sort of thing during war if they were ‘down.’

We see the impact of horses on training methods, equipment and armor used to ride them (part of the material culture of chivalry). For instance the Book of Marchalsi encourages gentle handling of horses and a light bit. Xenophon himself encourages a light hand to have the horse behave more magnificently. These are just examples of the back and forth conversation between the two species though. There are countless examples. A specific example from my article: “

Indeed the bit, is often associated directly as a means of teaching chivalric behavior.  Ramon Lull in his chivalric manual says the bridle and the horse can teach the knight how to restrain his behavior by not speaking falsely or being overgenerous. “And by the reins is signified to the knight that he ought to be led overall where the order of chivalry will lead or send him. And when it shall be time of necessity to make largesse, his hands must give and dispense after that which pertains to honor, and that he be hardy, and doubt nothing of his enemies, for doubt enfeebles strength of courage.”  The behaviors Lull describes—restraining speech, restraining charity, submission, largesse, and courage —are important ways of understanding how medieval authors saw and understood the equipment of the horse. Lull could observe that the bridle and reins are used to guide the horse but can also inspire courage in the horse so that similar values could be practiced by the rider as well. Xenophon made a similar observation: 

If you desire to handle a good war-horse so as to make his action the more magnificent and striking, you must refrain from pulling at his mouth with the bit as well as from spurring and whipping him. Most people think that this is the way to make him look fine; but they only produce an effect contrary to what they desire,—they positively blind their horses by jerking their mouth up instead of letting them look forward, and by spurring and striking scare them into disorder and danger.

Proper and moderate restraint is encouraged of horse and personal behavior is encouraged by both Lull and Xenophon. Again, reading horses and reading about horses would let the chivalric classes know how to modify their own behaviors, with horses and with each other. One can see that Lull, who was a knight, sees the bridle as important for guiding a knight’s own communication with his fellow humans and with horses. The whole is seen as a guide for behaving chivalrously.”

There is also the example I mentioned at the end of the roundtable with Alexander the Great and his father from Plutarch’s Life of Alexander (popular in the Middle Ages) where by observing how well Alexander handles Bucephalus, Philip insists he should rule a kingdom because good horsemanship equates to the ability to rule wisely. There are some great examples of modern ‘chivalric’ horses like Sgt Reckless whose story is sad and inspiring at the same time. And the romance of Bevis of Hampton and his horse Arondel ties the horse into chivalric culture and ascribes chivalric behavior to the horse very well.

In romances, equipment is often mentioned as part of a horse’s description, as in Sir Gawain and the Green Knight, as well as many other medieval romances. Still, I am not sure it always goes with the horse – it may go with the rider, too, as when the horse is killed. There is evidence of the equipment going with the horse, however, outside romances. In early medieval hagiography, for instance, a horse can be donated with its equipment, or the bridle specifically, as in the life of Bishop Aidan, reported by the Venerable Bede. I have a short blog on this: https://thegrailquest.wordpress.com/2018/10/19/a-horse-and-a-kingly-bridle-or-a-story-of-christian-generosity/

That said, in many cases, the equipment seems to increase, or at least highlight, the horse’s value in the eye of the beholder. 

In the chapter for The Horse in Premodern European Culture, I have looked primarily at 13th- and 14th-c. English documents, which provide very few details about specific horses: usually its type (destrier, palfrey, courser, etc.) and, sometimes, its colour. There is no information about markings or whorls. However, other sources, such as romances and hippiatric treatises or lists of horse properties/hierarchies of horse colors do mention some markings, such as white on the legs, blazes, etc. These white markings may have an effect on a horse’s qualities, such as its character, physical characteristics, or simply luck. Thus, a “coal-black” horse, with no white whatsoever, was thought to be in some way demonic and was to be avoided, as it might kill its rider, e.g., by drowning it. A very curious instance, discussed by Elina Cotterill in her paper in the volume, is the recipe for making a white mark on a horse – it means actually burning a horse’s skin with chemicals, presumably in the hope that the newly grown hair will be white. The purpose of this is unclear. I did not find any information about whorls and their relation to quality in European context, but I have consulted mainly English and French sources.

We notice the progressive come back of wooden bars on 17th century saddles, and La Guerinière, in his Ecole de Cavalerie (1733, p49), mentions explicitly the problem of iron bars, saying that this is an old practice that could still be seen in some provinces. (see also my chapter p 195)

The EHC, of course (See the EHC Resources page for more)!

The Facebook group “Horse History in the Middle Ages and Beyond” was initially created for the panelists in the International Medieval Congress equine sessions, but open is now to all.

A few other Facebook groups, especially “Horsy HEMA” and “Medieval Horse Equipment 1100-1530” might be of interest.

Anastajia Ropa has a personal blog (The Grail Quest) where she writes about horse history themes (but not only) now and then, in a less academic way.

Miriam Bibby also has a “horsey” blog: History on Horseback.