“I dismounted and took the saddle from my noble horse, he lay down at once. I took the bit gently from his mouth, and when he lifted up his head in pain and tried to rub it against me in mute appeal for help it seemed to me that tears were gathering in his eyes: it may be they were those in mine.”

- Henry Kid Douglas, I Rode with Stonewall, 1940

This quote is from the memoir of Henry Kid Douglas, a Confederate officer who did indeed serve with Thomas “Stonewall” Jackson. He wrote a memoir of his experiences that was published several decades after his death in 1940. Though I won’t be talking about European knights as was originally asked in the question, but since you allow other time frames as well I can explore a bit about troopers attitudes towards their mounts during the American Civil War. Suffice to say Confederacy or Union, troopers certainly did bond with their horses and regretted their deaths. From the Union side:

“I stood there looking him over, saw him bleed and then boohooed like a child; I cried as if I had lost a brother; he had been my most faithful, playful friend, my good reliable carrier and companion for many months, and to care and feed him with the best and with my own rations when nothing else was left, had been my pleasure.”

- William E. Meyer, The Sailor on Horseback: Personal Narratives of Events in the War of the Rebellion, Being Papers Read Before the Rhode Island Soldiers and Sailors Historical Society, 1912

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“…for a while my own danger forgotten in sympathy for the poor horse. He had borne me faithfully and well through a thousand perils, and now he was giving up his life in my service. I am not ashamed to confess that the expiring breath of Shiloh as it ascended from those wild woods wrung from my eyes a tear of anguish and regret, though long a stranger to the melting mood.”

- John A. B. D. Williams, Leaves from a Troopers Diary, 1869

Likewise, it was never limited to just enlisted men. Officers certainly developed emotional attachments as well as shown above with Douglas or as follows with Sherman.

“You will be pained to hear that Duke is dead…I never had a horse that suited me so well as Duke, and I was indebted to you for him, and it gives me real pain to tell you of his death.”

- William T. Sherman, W. T. Sherman to Frederick Steele, 2 January 1864

Though we may wish that these were the only attitudes towards horses in the conflict, there were also cases of soldiers who neglected or abused their mounts. In some cases, it was to avoid duty and in others it was because they had a difficult horse. Despite still being in the era of horsepower (in the sense that they were still a major form of transportation), the Union actually had a relative lack of competent horsemen and riders. Many could drive horses quite well, but riding was actually a separate skill that not all northerners, particularly from the urban settings, had.

As a result, inexperienced horses and inexperienced men did not make for a pleasant experience, with some resorting to abuse to solve their “difficult horse” problem.

“There the poor brutes had stood for ten days, without food or water, until one had died in the agonies of starvation, and the other, having gnawed up all the trees around him, was reduced to a walking skeleton…the fate of such men if captured…is not to be envied”

Charles Francis Adams, A Cycle of Adams Letters (from Common Soldier Uncommon War 1920)

There are many more examples that I could quote for both kinds of men, those who when mortally wounded cried out first for their horse, and those who either “deemed it policy to kill [the horse] as quick as possible and take the chance of getting a better one” or had to be punished in some way for treating their horses in a brutal manner. The Civil War is not unique in this either as I have seen the same two attitudes in conflicts such as the Boer War of South Africa. The fact of the matter is that the horse has both served alongside men in 5000 years of conflict, as well as have been our victims of the same. Brother in arms or casualty of war, they were not to reason why.