I’ve been driving for an hour and a half on wide and dusty roads and have barely seen another vehicle. Far behind me are the fumes and frustrations of the traffic jams that snake through Mongolia’s capital city, Ulaanbaator.

Surrounding me now are only the vast empty spaces and dramatic mountain ranges of central Mongolia. And there are horses, too – lots of them. The only place on earth where there are more horses than people.

Mongolia has an unfaltering love affair with the horse that has lasted centuries. And with over three million of them, this is a place where horses really are everywhere.

In the distance I see men, either on their own or in pairs, herding sheep and cattle on horseback. Closer by, tucking into scratchy tufts of grass poking through the sandy ground at the side of the road, large herds of horses form unwieldy lines which spill on to the road in front of me.

Making my way slowly through this horsey gridlock, I am struck by their variety. Like a jumble of breeds brought randomly together on the wayside, they come in all sorts of colours and sizes – from jet black to pale amber, some with rough coats, others with smoother hides – no wonder the Mongolians have more than 500 words to describe the coats of their horses.

But while these horses may all look different, under the skin they are, in fact, all the same. All are domestic horse breeds. Just like America’s famous mustang, these horses may appear to be wild but they aren’t. They have simply become feral – domestic horses originally bred and kept by humans that now happen to be living in the wild.

To find a truly wild horse, I need to drive another half an hour or so to the Hustai National Park, 60 miles south-west of Ulaanbaator, where, under the shadows of the Khentii mountain range, they roam freely.

Known in Mongolian as takhi, these horses predate the evolution of the domestic horse. The only living link between the world’s first horses (the extinct hyracotherium), which galloped the earth some 55 million years ago, and today’s domestic horse, takhi – with a different chromosome count to domestic horses – are the world’s only living genuinely wild horse.

While around 60 million domestic horses are now found around the globe, only a few hundred takhi survive outside captivity. An endangered species, takhi are found only in Mongolia, most of them here in the magnificent steppe landscape of the Hustai National Park. Steppe (arid grassland and salt plains) once made up a quarter of the world’s vegetation but, in its original form, can now only be found in Mongolia.

On the plains of Hustai there are more than 450 plant species, many perfect fodder for takhi. But as well as the grassy steppes, there is mountainous forest here, too. And it’s in the forest that my search for takhi begins.

Accompanied by Serjee Tserenhadmid – a young Mongolian woman who has known the land here since childhood – I pass hundreds of tall, eerily pale birch trees which line the sides of the Hustai’s quiet mountains like a ghost forest.

Branches lay fallen and trampled on the ground; bark reveals the unmistakable indent of horse incisors – both recent signs that takhi have been here snacking here. At night, wolves, foxes and lynx chase through these trees hunting for evening meals of gazelle and red deer.

Dodging the holes of marmots (beaver-like mammals) we head out of the forest and down to the empty plains below. A golden eagle flying above us does the same. As he passes out of sight, we see instead a small herd of horses grouped around a wide river where the last snows of winter are melting.

“Takhi,” says Serjee excitedly. I follow her as she quickly heads off to the river. Just feet away from them, we stop, catch our breath and stare at the takhi in front of us.

Short, chunky and muscular, these horses look very different to their domestic cousins, with huge nostrils and large, rectangular faces. Their handsome heads are supported by thick necks; stubby ears are full of straw-like hair; and manes are upright and stiff like those of zebras. More Popeye than pretty, takhi are strong horses engineered by nature to survive earlier, tougher times.

Made up of one stallion, mares of various ages and some of last year’s foals, this is a harem of 10. During Mongolia’s frozen and snow-filled winters, takhi coats turn cream for camouflage. As summer approaches they darken gradually to a soft brown. Now it is springtime, and they are wearing their “between seasons” coats of butterscotch, caramel and toffee.

While takhi may come in confectionary colours, their nature is not so sweet. During the mating season, stallions will kick each other to death to gain dominance; when wolves threaten to take foals, takhi will rear fiercely to protect their young; and no man – except, if you believe the legend, Genghis Khan – has ever been able to ride one. Unknown to Europeans until 1878, takhi are as wild as the landscape they live in.

Whinnying and neighing, the takhi are becoming restless at our presence. The stallion rises on to his hind legs, snorts noisily and starts to move off. Breaking into a collective canter behind him, unfettered by man or saddle, the harem vanishes quickly into the wilderness. Serjee tells me that in Mongolian takhi means spirit. After what I have seen today, there’s need for her to explain why.