PHIDIPPIDES (in his sleep): That's not fair, Philo! Drive your chariot straight, I say.
STREPSIADES: This is what is destroying me. He raves about horses, even in his sleep.
PHIDIPPIDES (asleep): How many times round the track is the race for the chariots of war?
STREPSIADES: It's your own father you are driving to death....to ruin. Come! what debt comes next, after that of Pasias?....Three minae to Amynias for a chariot and its two wheels.
PHIDIPPIDES (asleep): Give the horse a good roll in the dust and lead him home.
STREPSIADES: Ah! wretched boy! it's my money that you are making roll. My creditors have distrained on my goods, and here are others again, who demand security for their interest.
The Clouds, by Comic Genius Aristophanes .
Chariot racing was one of the most important events in the Games (see post below). It was sort of like NASCAR -- an expensive, extremely dangerous spectacle very popular with the public.
Horses are an expensive business and that was especially true back in the day. First you needed to actually purchase the beast from its native home of Thessaly or Argolis. Then you'd need land (and stables?) to keep them, handlers to train and exercise them, slaves to tend to their impossible feet, gear for leading, riding and grooming them...and that's without all the other add-ons such as cheek pieces for battle and pimped-out chariots for cruising.
Owning a horse and being part of the cavalry, therefore, was a sign that you belonged to the elite. What's new? The equestrii were Rome's landed gentry, medieval knights had special status (chevalier is still an honorific) and Prince Charles plays polo. The connection between horses and kudos is clear in another quote from The Clouds, where Strepsiades moans about how his status-hungry wife is responsible for his son's hippomania:
[W]hen we had this boy, what was to be his name? It was the cause of much quarrelling with my loving wife. She insisted on having some reference to a horse in his name, that he should be called Xanthippus, Charippus or Callippides. I wanted to name him Phidonides after his grandfather. We disputed long, and finally agreed to style him Phidippides....She used to fondle and coax him, saying, "Oh! what a joy it
will be to me when you have grown up, to see you, like my father, Megacles, clothed in purple and standing up straight in your chariot driving your steeds toward the town." And I would say to him, "When, like your father, you will go, dressed in a skin, to fetch back your goats from Phelleus."
Alas! he never listened to me and his madness for horses has shattered my fortune.
Only the rich could afford horses, but only the disgustingly, filthily, orgiastically rich could afford racing horses. The usual costs applied but then they had to shell out minae for a nice little jockey-slave, a two-wheeled chariot, space to train in and (presumably) guard-slaves for their four-legged assets. Not only that, but they had to expect that both the horse and its jockey would be seriously injured sometime soon. Athenians had access to specialist horse doctors hippiatroi  but they had to be prepared to sustain a huge loss.
The reason injury and death were so likely becomes obvious when you consider the incredibly tight turns the chariots had to make at very high speeds and in close proximity to other drivers. If you want a sense of just how tight the turns were, have a look at this imaginative video reconstruction of the Hippodrome of Byzantium. Although it was built nearly 1000 years later than the Classical period, it preserves the Greek plan perfectly.
Incidentally, the site of the Olympic Hippodrome was a mystery until just last year, when some German scientists located it with radar . The Olympic Hippodrome is where the victory that Pindar celebrates here was won:
Olympia IV: Processional for Psaumios of Camarina: Victory with Chariot 3
Charioteer on high, your team has hoofs of thunder --
O Zeus: for again these are your Hours,
That to my lyre dance, my dappled song,
Who circle, who summon me
Bear witness here at this highest of Contests.
A friend fares well; true friends rejoice,
And the news is sweet.
Ah yes, O Cronos' son, who lord Mount Aetna,
Windswept trap to clamp down storming hundred-headed Typho,
Consecrate your Olympic
Victor; grace these our revels --
Light most late, far-shining burst of sun's
Strength, excellence: Psaumios has come!
He is riding by; the olive of Pisa crowns him:
May Camarina awake
With him to glory; may god grant
Fulfillment to his prayers! Hear his eulogy: he has raised
a line of thoroughbreds;
Philanthropist, all strangers are his guests, his land asylum;
His motto: Peace, not Politics -- Civic Concord, Patriotism!
No lie shall taint
My praise: No, for truth will out.
It happened so with Clymenos' son.
That Lemnian women
Scorned his love -- at first.
But then he won the race, all brazen in his armor,
And spoke thus to Hypsipyle, when he came to get his crown:
"Well, here I am: you've seen me run!
And heart can equal legs.
Often the hair grows grey -- too soon,
Belying a young man's age...
It just occurred to me that this last section might be some kind of joking allusion to how an old guy can attract hot chicks if he wins a drag race. It also reminds me of how I heard a nerd in McDonalds say to his buddy, "She was an older lady but...snow on the roof and a fire in the furnace, ya know what I mean!"
2. p.54 Animals, Disease, and Human Society By Joanna Swabe
3. Psaumios was probably the owner, not the rider. Riders could be family members but were more often slaves. Probably they were often teenagers (like the one sculpted above) as lightness was an advantage.
4. Discovery of the Hippodrome
5.from Selected Pindar Odes translated by Carl A.P. Ruck and William H. Matheson.