It is a bad time to be making a giant horse. But are there ever any good times? Artist Mark Wallinger and his funders face a struggle to pay for the colossal statue of a white horse that he has been commissioned to create as a public artwork at Ebbsfleet. The idea was hugely popular when he won a competition for the job, and yet in these times ... well, it's a slog to get the cash. But as I say – has there ever been an opportune moment to make a giant horse?

"I know what the times are like ..." wrote Leonardo da Vinci to his employer Ludovico Sforza, ruler of Milan, in the 1490s. He was wanly conceding that money for the Horse might not be forthcoming. The Horse – Da Vinci's horse – was a towering equestrian monument that he planned to cast in bronze as a memorial to Ludovico's father, Francesco Sforza. It was one of the projects he proposed to take on when he first asked Ludovico for work in the early 1480s. It became perhaps the most famous of all his activities in Milan, alongside his other epic work in the city, The Last Supper. But when he finally abandoned the defeated Sforza and fled Milan at the end of the 15th century he left behind only a grandiose clay model of the horse. It is said that French archers used it for target practice.

This unfinished masterpiece has haunted the centuries and will surely haunt the banquet of an exhibition about Leonardo da Vinci in Milan coming to London's National Gallery this autumn. When he left Milan the artist and engineer took with him many drawings for the Horse. Those that survive, in collections from Windsor to Madrid, range from studies of equine proportion to designs for complex casting machinery. Leonardo's project was scientific as well as aesthetic, a conscious attempt to work at the limit of existing technology and to rethink age-old traditions of casting.

His drawings of this never-completed creature are eerily beautiful, and plant the image of it firmly in the imagination. So why was it never built? He had some bad luck. In 1494 the political machinations of Ludovico Sforza played a part in causing a French invasion of Italy that turned priorities upside down. A stash of bronze set aside for Da Vinci's sculpture was needed instead to cast cannon. The expense of war then made Sforza unlikely to fund the gargantuan work. Yet even before that, Da Vinci's employer seemed to doubt if he was serious and sought out other potential horse-casters.

The unmade Horse is the work, more than any other, that epitomises Leonardo's reputation as an artist who never finished anything. When he returned to his home city, Florence, the young Michelangelo was waiting to insult him as the fraud who had promised to cast a great bronze horse but gave up in shame.

And yet – more than 500 years after he designed it – Da Vinci's bronze horse still tantalises the human imagination. A work of art that exists only as an idea, documented in his scintillating, dreamlike drawings, it is arguably the first conceptual artwork. Or the first surrealist dream object. Whatever it is, the horse that never was will always be remembered with more clarity and emotion than most existing works of art. It is the image of Leonardo da Vinci, the quintessence of his unique quality.