Training! While horses are well known for preferring to flee at invisible squirrels, they can be trained to not react to gunfire; which proved to be a necessity after the introduction of the firearm. However, pre-firearm battles were still loud affairs so the training to handle guns was not as new of an invention as the guns themselves.
For United States Cavalrymen in the Civil War (1861-1865), the Regulations and Instructions manual of 1862 had a section on training young horses. Horses were trained by the troopers of the units themselves and overseen by officers. The method of training them specifically for gunfire was given as follows:
Manner of accustoming Young Horses to Firing, and Military Noises.
A few trained horses, accustomed to the firing, are mounted with the young horses; toward the end of the lesson, the troopers who mount the former separate themselves a few paces from the others and fire pistols, while the others continue to march on the track; the troopers taking care to quiet and caress those which are excited or frightened.
Horses are herd animals which is why having trained animals, having already gone through the training, can keep the herd calm. They are very responsive to the body language of each other which is why seeing seemingly calm horses within the herd can keep the herd calmer as a whole. The soldiers themselves, in handling and caressing the animals, also function to keep them calm.
This method is continued during some days, the troopers approaching nearer and nearer, and finally firing inside of the square; they fire afterward when returning to the quarters at first in the rear of the column, then near the centre, and at last at the head, facing it in the distance of a few paces.
There will be an interval between the shots at first, and they will be fired more frequently in proportion as the horses become more calm, taking care not to burn them with the grains of powder.
When the young horses are somewhat accustomed to the noise of arms, the troopers who ride them, having loaded their pistols between the lessons, fire one after another at a signal from the instructor.
This lesson should be given with care, the firing being stopped when the horses become excited; after they have become more calm, the shots are repeated with shorter intervals. The carbines are afterward used.
Troopers start the horses with pistols at various distances and locations around the herd, stopping when the gunfire excites any of the horses. Once horses are calmed, then they continue. This is repeated until the horses stop reacting to gunfire, after which they move to larger weapons like carbines.
Should there be any horses so restive as to throw the others habitually into disorder, they must be sent back to the stable; they are taken out separately, every morning and evening, to accustom them to the noise of the arms. For this purpose they are led to the riding-ground, where pistols are fired while they are caressed, and a few oats are given them. The shots are first fired from a distance, and approach gradually. After the horses become accustomed to them, they are joined to the others, to receive the same lessons when mounted.
Some horses may be more difficult than the others to acclimate, and an excited horse will affect the entire herd. Removing such horses from the herd enables the training to continue for the majority of the mounts while the problem equin can be individually trained and reintroduced to the herd when the training permits.
When horses are no longer frightened at the successive carbine or pistol shots, they are formed at the end of the riding-ground; they are marched gently toward some dismounted men placed at the other end, who fire together several times in succession; when the horses are within fifty paces, the firing ceases, and they are marched on until they come up to the men, where they are halted and caressed.
An officer is always present at this lesson, to see that it is given properly and without disorder.
The young horses are likewise accustomed to the manual of arms, the waving of standards, colors, and the flags of lances, to the noise of drums, and finally to all military noises, This is always done at the end of the lessons, the same progression being followed and the same gentle means used.
Essentially this strategy is just acclimation and exposure, which is a not a new idea for training horses as even Xenophon suggested it. For gunfire specifically, eventually horses realize that the noise won't really hurt them and some of them will find themselves used to train the next generation horses. There really isn't a complicated science or technique behind this beyond just patience and perseverance.
Source:
Regulations and Instructions for the Field Service of the US Cavalry in Time of War. McClellan, George B. Philadelphia. 1862
If you are interested, my previous answer on horsemanship manuals for the ancient world.