When the dance first began in warfare is unknown.
According to the Encyclopedia Americana, the use of horses in warfare dates from around 1700 B.C. with the use of war chariots in Mesopotamia.
I think we can be fairly certain that, when engaging in battle, humans will use anything they can get to startle, damage and/or overrun the enemy. According to the Encyclopedia Americana, it was approximately as much as 5,000 years ago when barbarous tribes in central Asia began herding horses for food. For someone who has been around various types of horses with various types of training, or no training at all, it takes no stretch of the imagination to think that one or more of these primitive horse herders got kicked, bitten, struck or shoved into the briar patch and stomped on, and the next time one of these herders got into a fight or fought in a tribal war, s/he thought how much this element would be useful to them if only they could put this handy resource under their command. Also I would think that the blood lust or survival drives in these primitive peoples would put writing this all down for posterity in a relatively minor slot to not at all thought about. Therefore I think it's safe to say that horses in battle probably predate 1700 BC and the chariots.
Long before the Birth of Christ, the Berber warriors and their mounts, the Barb horses, were famous. These warriors rode into battle with no bridles or saddles and together with their horses, having the conformation and attitude for the intricate equine battle movements, struck fear into their opponents.
If one watches these ancient breed type horses at play, one can see all the battle movements now known as the 'Corbette', 'Capriole', 'Lavade', 'Canter Pirouette', 'Piaffe', 'Passage' and others. The conformation of the ancient Barb type horse supports these movements better than any other equine. Unfortunately, in modern times, this ancient breed type is being crossbred into extinction and the battle movements are deteriorating with the loss of true ancient breed type.
Barb type
Turkoman type 
The three foundation sires of the
popular Thoroughbred horse of today. No record was kept of the breed
of the mares because a female was considered simply an incubator.
Such ignorance of genetics loses us the actual gene pool of the Thoroughbred
horse of today.
Now it is known that the female
actually contributes all of the mitochondrial DNA as well as 1/2 the nuclear
DNA while the male only contributes 1/2 the nuclear DNA.
One thousand years after the historical
mention of the famous Barb horses, another famous war horse is mentioned,
the Arabian. This beautiful breed was used in war for the fast passing
strike. The Arabian was bred for speed and endurance and not for the close,
prolonged fight of the earlier Barb. Built almost entirely opposite from
the Barb, these beautiful horses were formidable against foot soldiers
and later the heavier armored horses.
The Turkoman was also an ancient
war horse especially noted for their strange shiny coat color. Similar
to the Arabian, but with notable differences. Nomads trained themselves
to shoot the compound bow while guiding their horses with their legs.
(note: At the old Ivory polo grounds in Detroit, MI there was a polo pony called Cobra because of the actual shape of a white cobra on his forehead. This horse was considered a dun/buckskin because of his light brown coat with black mane, tail, stripes on his knees and hocks and stripe down his back. His coat was actually the color of a new copper penny and when the sun shone upon it no one could look at Cobra because of the reflection of his coat. No other horse had his striking coat color and not until my research happened upon the Turkoman horse did I understand that Cobra must have some of this blood in him.)
The ancient Celts fighting from chariots would, having a charioteer (or not), climb onto either the tongue (bar between the horses) of the chariot or up onto the horses backs to fight. Riding two or more horses in this manner is called 'Roman Riding' and was used to entertain the crowds at the Roman circus. (photos on the photo page.)
The counter to the well trained fighting nomads was, of course, armor. The Encyclopedia Americana states that the Assyrians experimented with armored horsemen as early as the 8th century B.C., but the full development was in Iran, where cataphracts - armored archers on armored horses - were introduced ~530 B.C.
LET US NOT FORGET THOSE HORSES OF EITHER BREED, ANY BREED, OR MIXTURE THEREOF, WHO WENT INTO OUR ANCIENT WARS TO FIGHT WITH VALOR AND DIE WITH HONOR.
Music is an excerpt from "Brian Boru's March" from Carol Thompson's CD "The Faerie Isles" (Dorian Recordings)
Title clip art is from http://www.horsegallery.com/index.htm
Barb home pages at: https://www.angelfire.com/ky/WarHorse(Spanish Barb War Horse)
and http://www.geocities.com/Athens/3240(North African Barb War Horse)
Turkoman graphic from: http://www.turanianhorse.org/euram.html
