I call my palomino mare Spirit because she is the same colour as the stallion in the kids’ cartoon film. Don Gilberto, the rotund schoolteacher from the lakeside village of Coquinal who hired us the four horses, gets the joke. He’s seen the movie.

My Spirit has none. She ambles forward, eyes cast down, at a very slow walk. Don Gilberto rides up behind her and lashes at her rear with his rawhide whip. We have been riding for two days since canoeing around the edge of Lake Rojo Aguado. This is not simply to indulge my boyhood fantasies of riding the pampa gaucho-style. With no motor transport available, this is the only way to carry our gear across the savannah.

Horses sweat: they don’t show that in cowboy films. Nor do they show that if you are to carry a meaningful amount of food and water in order to survive the apparent emptiness of the grasslands, let alone a rolled-up portable canoe, your horse’s speed is so greatly reduced that you could walk faster. Still, at times, it’s enormous fun. Yesterday, just before sunset, we spotted a shaggy red-maned wolf and chased it, barely breaking into a trot.

It seems incredible that only three days ago we were still canoeing the lake, weaving between the palms at the water’s edge rather than cutting across the open bays where huge swells spring out of nowhere at any boat attempting the crossing. We knew if we capsized we would certainly lose all our belongings; possibly we would meet the caymans we had spotted sunning themselves on the islets formed by root masses clustered around the bases of palms.

For three nights we have slung our hammocks in the soggy forest at the lake’s edge, relaying daily reports via satellite phone to a summer school project in Knowsley city learning centres. As they are also working with a jaguar reserve in Brazil, we want to impress them with big cat sightings.

We have had none yet. The best I could do was make a cast in plaster of Paris of a jaguar track I found in some mud close to one of our camps. But there’s time yet, and as this savannah and wetland habitat is prime jaguar country, we think our chances are very good.

Don Gilberto says we were lucky on the lake. The wind had come from the south. If it had come from the north, we might have been stuck for days.

He knows little of the Moxos civilisation, whose land we are crossing, because the oral tradition of the Movina and Payubaba people at Coquinal only records as far back as when the Jesuits were here 300 years ago. But he does know that ruins, or artefacts such as clay pots (he is unclear about this), have been found at Lake Huachuna, which we passed yesterday.

“That hill might be something to do with the people before,” he says, pointing to a flat-topped rise in the ground. The only elevation in an otherwise flat country, it must surely be man-made.

But it’s late, and we must find water and forage for the horses before dark. So like my hero in the cowboy film, I spur my Spirit on and we ride off into the sunset.

Simon Chapman is head of physics at Morecambe high school and author of the Explorers Wanted! series for children (Egmont) and The Monster of the Madidi (Aurum Press). Follow his progress for the next three weeks in The TES and keep up with the Knowsley project at www.spiritofthejaguar.org.uk