Mark Wallinger's vast white stallion is already the runaway favourite in the race to build the new £2 million sculpture at Ebbsfleet International Station in North Kent. It deserves to win by a mile, and not just because it will be 164ft high.

The idea of creating an enormous horse in the middle of the English countryside is so brilliantly obvious it is a wonder this has not been done before. (And it has, of course: there are some 21 white horses carved into chalk hillsides across England, the earliest being the Uffington horse in Oxfordshire, a great cantering horse-god scooped out by prehistoric hands.)

No animal is so deeply embedded in British culture, history, self-image and language. We look gift horses in the mouth, get on our high horses, stand tall in the saddle and horse around. And the arcane, ancient language of horses and horsemanship is the everyday language of people who would never sit on one: reins, bridle, girths and bits between our teeth.

We see white horses on our seas, and measure motor strength by the power of horses. We fit horses perfectly. “Man, a little lost on an elephant, is seen to his advantage on the horse, a throne truly to his measure,” wrote the French poet Francis Ponge.

The dog is Man's best friend, but our most valuable relationship with any animal has been with the horse. From the Celtic horsemen riding out against the Romans in 55BC to Thelwell's enduring cartoons, we measure our world through horses: the medieval warhorse, the plough horse, Betjeman's luckless Diana whose “ponies have swallowed the bits/ She fished down their throats with a spanner/ And frightened them all into fits.”

We have been venerating horses in art as long as we have ridden them. The earliest example of art ever discovered in Britain is a flat bone with a detailed horse's head carved into it, believed to date back to 10,000 years BC. Artists have always been drawn to catch the horse: the marble horses on the Parthenon, da Vinci's sketches, the drawings of Degas, the paintings of Gainsborough and Constable, and above all George Stubbs, who understood the nobility and anatomy of the horse better than any other artist.

The familiar sight of a horse in a field evokes the quintessence of English rural life, rekindling ancient feelings long after the horse has ceased to be part of our daily lives. If Wallinger's design wins the commission, Eurostar passengers will be able to enjoy the same view, only 33 times larger than usual.

But he may be backing the wrong horse. For a start, his computer-generated stallion looks exactly like a gargantuan version of my old Action Man horse, stiff-legged and lifeless, likely to topple over at any moment and bring down a pylon. Stubbs's famous painting of Whistlejacket, the rearing chestnut stallion painted in 1862, was so lifelike that the real Whistlejacket tried to attack it, mistaking his own image for a rival. Wallinger's Dobbin, by contrast, looks bored and slightly knackered, unlikely to attack anything.

But it is not the appearance of Wallinger's horse I object to, so much as the breed. I am no expert on horseflesh, but this animal looks to me like a thoroughbred, a racehorse, an expensive creature built for speed and pleasure. It is, in short, an elite horse and, like all thoroughbreds, descended from imported Arab stallions.

A better representation of essential equine Britishness would be a sculpture not of a racehorse but of a pony: a tough, sturdy, low-slung, hairy and adaptable creature that more nearly reflects our national character.

For centuries, horses have been linked to aristocracy. The poor fought on foot, the rich from horseback. Henry VIII imported heavier horses from the Continent to bulk up the local stock, and fined breeders who sold foals under 13 hands. Pony races, the entertainment of the lower classes, were sometimes banned in the 18th century. Horse riding is still often seen (usually by people living in cities) as elitist: the bizarre and pointless battle over fox-hunting was as much about the social associations of horse riding as the ethics of the blood sport.

But for most of British history, the connection between Man and horse has been a working relationship. The horses that truly represent Britain are the carthorses, Shires, Suffolk Punches and Clevelands that pulled and ploughed and reaped, or the sure-footed pit ponies working underground and scenting danger. Too often forgotten are the warhorses that carried men and arms into battle: more than 700,000 British soldiers died in the First World War, and more than a million horses with them. Then there are the sturdy Highland ponies built to drag food off the hills, and Shetlands with adapted nasal cavities to warm freezing air before it entered their lungs and thus able to work when other horses would fail.

Though the numbers are dwindling, Britain has a wider variety of wild ponies than anywhere else in the world, and none is more perfectly adapted to its environment than the Exmoor pony, the purest of the remaining wild breeds. This is an animal designed for rain, with a double coat (soft inside, oily outside, a sort of Barbour on legs), an “ice tail” that channels water away and an extra rim of flesh around the eye socket, a “toad eye”, to keep out the driving rain of the moors.

Wallinger is planning to scan a picture of a live stallion into a computer on which to model his huge horse. How fitting it would be if, alongside the great racehorse, there could be a native workhorse, or a rainproof pony: smaller, more rugged, less elegant, but closer to the horse of our collective history.

In our dreams we are a thoroughbred race, but in reality we are pony people, and all the better for it.

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