'I didn't meet Marlboro Man, but I rode Marlboro Horse'

Here is a fine way to lower your children's holiday expectations: tell them there is no swimming where you are going, no thrill rides, no television and no video arcade or disco. It is, in fact, 20 miles to the nearest shop of any description. You might add that the trip will be educational and they will be taking lessons. At this point, of course, they may well rebel and refuse to come with you to the airport.

Force them on to that plane, however. For taking them along to this place they will surely thank you. I don't think my son and daughter, aged 11 and seven, have ever come home from a holiday more excited about their experience. We have just been to a dude ranch.

Playing cowboy in the American West had long been on my holiday wish list. I had hesitated for years, partly because I wasn't sure which ranch to choose. (The ages of the children were a factor, too.) Finally, in a fit of carefreeness, I picked the first one I could find on the internet. It was called the Bitterroot Ranch – it comes high in the alphabet – and it was in Wyoming, a state that I love.

This will sound cheesy, but I make no apology. I could not have made a better choice if I had researched dude ranches for a lifetime. I thank the internet gods for directing me to Bitterroot, to its owners Bayard and Mel Fox, to their many wranglers who look after the horses and guide guests on their rides, and, most importantly, to Blondie and Jasper, my trusty steeds.

Every visitor to Bitterroot is assigned at least two horses for the duration of their stay. It says as much in the information package sent to you after booking, which also conveys clearly that the ranch is serious about riding. We were to arrive with riding boots, which required a quick stop at a Western-wear store when we flew into Jackson Hole, a tourist town under the Teton peaks in the Rocky Mountains.

All this was enough to make the three of us a little nervous. Between us, we had probably been on horseback for about 10 hours in our lives. Sitting in the taxi for the two-hour ride from Jackson to Bitterroot, I wondered what I had done. Did they know how useless we were? My worries deepened as I surveyed the landscape, which became more arid and brutal the further we got from the Teton range.

The last 16 miles to Bitterroot are travelled on a gravel road, heading north towards the Absaroka Mountains and the fringe of the Shoshone National Forest. When finally we found the ranch, verdant along the banks of a rushing river, reassurance flowed. We spotted the main corral and an antique wooden barn, the point from which every ride during the coming days would start, as well as the building that was clearly the main lodge. Tiny cabins were dotted about; one, we knew, would be home for a few days. To the delight of Polly, especially, there were animals everywhere: goats, geese, dogs, peacocks, three revolting-looking turkeys and a pair of shaggy llamas.

Bitterroot is an entirely relaxed place. Mel and Bayard are strict about only one thing: the welfare of their horses. Indeed, their reputation in this regard is the main reason for many of their guests choosing Bitterroot over other ranches. Many ranches lease their mounts just for the tourist season, but Mel and Bayard own their horses and know all 150 by name. Guests will never be berated for not changing before dinner in the lodge (or wine and hors d'oeuvres at 6pm), but they will be scolded for failing to stand in their stirrups when their horses take a pee.

Other than that, you are obliged to do nothing at the ranch. You don't even have to ride if you don't want to, but I can't imagine travelling all that way and not giving it a go. If you are a beginner, as we were, have no fear. Lessons are given in a ring on Tuesday and Thursday mornings. Other times you will be on rides out into the Absaroka foothills with wranglers giving you tips on what to do. By the end of our four days, Polly was comfortable trotting while Jonathan and I found ourselves cantering through the sagebrush, grinning madly from the thrill. One morning, they actually had us driving cattle, a group of bullocks that had crossed into the ranch from the neighbouring Indian reservation. Yee-haw!

Mention City Slickers, the Billy Crystal comedy that made dude ranches fashionable 10 years ago, and the Foxes will grimace. Mel, who was raised on her family farm in Tanzania and educated in England, is dismissive of the notion that a few days at a ranch will turn any urban dweller into a ropin', gallopin' cowboy. Bayard, hugely tall, kindly and in his early 70s now, is similarly unimpressed. But, heck, a bit of John Wayne dreaming never did anyone harm. And in some ways, Bitterroot almost encourages the fantasy.

The land it occupies, for example, – some of it owned by the Foxes and some of it leased from the government – is real Marlboro Country. That is to say, Philip Morris has often come to Bitterroot to shoot its iconic ads. I made no attempt to disguise my delight when I was told that Blondie had often been used as the Marlboro Man's mount. (Who says I wasn't a real cowboy?)

There was no mistaking, then, that we were in the Wild West. On one ride, we diverted into some tall pines high above the ranch to view an old log cabin. Historians have suggested that this was a hideout used by Butch Cassidy.

Visit Bitterroot and you may or may not find other children there. Mine, who met only one other 10-year-old, considered it paradise regardless, and Bayard says he loves it when guests bring children. "I wish more came," he told me. "They learn so much faster than adults and they appreciate being out here, seeing the delicate balance of the environment and the slower pace of life." If your offspring tire of riding, – or lose their nerve – Bayard will find other things for them to do. He took us fly-fishing (this first-timer caught two large trout), and the day we left was preparing to accompany another youngster game shooting.

Now my children have given me a choice for next summer. Take them back to Bitterroot or buy each of them a horse.

The Facts

Getting there

Return flights to Jackson Hole cost £321 with Trailfinders (020-7937 6500; www.trailfinders.com). Arrange transfers to Bitterroot with the ranch.

Being there

A week at Bitterroot (001 307 455 3363; www.bitterroot.com) costs £1,000 per person, based on two sharing, including full board and six days' riding. There is a 15 per cent discount between 26 May and 16 June, or 25 per cent off for under-16s. Bitterroot's owners, Mel and Bayard Fox, also run Equitours (www.equitours.com), which organises riding tours worldwide.