'As in the drummer of The Who?" I ask. Keith Moon, a laid-back Montanan with a large-brimmed Stetson, chuckles. Presumably he does this whenever somebody comments on his name, though he must have heard it a thousand times. He tells me to follow him, then hops in a black pick-up and motors down the steep, one-way path to the main road. A few hundred yards on, we turn through an open gate and pull up next to a field. Remp, a beautiful 10-year-old quarter horse, is already saddled up and grazing in the shade of a Post Oak, waiting for me.
Keith jumps on Gracie and we trot together to another gate, across a field, over a stream and out into the Balcones Canyonlands. Keith is from Bozeman, Montana, but we are a long way from the mountain state – on a ranch in Texas Hill Country. Keith moved down here three years ago to work as the equine manager at Travaasa, a unusual resort 30 minutes north of the Texas capital, Austin, that marries guided adventures like this with holistic spa treatments and upscale dining.
I've come here for a spa weekend with a Texan twist: to enjoy the cowboy experience, but in the lap of luxury. Travaasa sits on one of numerous tracts that make upTexas's central Balcones Canyonlands Preserve, a refuge formed in the early 1990s to conserve habitat for endangered songbirds.
Anderson Mill, where Travaasa is located, may be a stone's throw from downtown Austin, but 150 years ago this really was frontier territory. The small town along Cypress Creek was named after Thomas Anderson who built a mill here in the 1860s to manufacture gunpowder for the Confederacy.
For some light reading, I've brought along a history of Texas and a book called The Prairie Traveler by Randolph Barnes Marcy, apparently the best-selling handbook for American pioneers in the 1860s. There's nothing like some revision before attempting to assimilate into the cowboy way of life.
When the American Civil War drew to a close, there was plenty of cattle here and not enough farms in Texas to buy them. So, in a move that has now become firmly bound up in the mythology of the West, cattle herders forged trails northwards to sell their stock.
One of the most famous of these, the Chisholm Trail, passed near here. Fuelled up on caffe latte, my horse saddled for me, I prepare to take a leisurely trot along a gentle path. I'm fully aware this wasn't quite the experience of the cattlemen that beat these ways before me. According to my book, "weary and battered men" endured months of "grinding, 18-hour days in the saddle, the misery of rainstorms and endless dust clouds … [blazing] the northern trails, through Indian territory and even more dangerous and avaricious whites".
Luckily there'll be no northwards trek for me today. Just a short ride around a pretty forest before heading back to Travaasa in time for a beer tasting.
Travaasa is all about the spiritual experience. On the purpose-built property, in addition to more active pursuits such as archery and ziplining, there's meditation, massage, yoga, hiking and even an ecology class you can sign up for.
In keeping with that theme, you don't just get to ride your horse in the Texas wilderness; you can also take the "equine experience" in which you learn to "join up" with an unbroken horse. (Remember The Horse Whisperer?) If you're not a horsey person, this involves standing in the middle of the manège with a whip, and spinning gently round with whip extended while the horse trots around the fence. You change direction and the horse changes with you. Stop, and the horse stops. Eventually, it will become submissive. You then put the whip on the ground and, when the horse turns its head towards you, you can walk straight up to it.
Next on the agenda for me is riding a mechanical bull. At Travaasa, "Brutus" is set up in the gym and I'm joined by seven women all on girls' weekends. Our instructor, Cathleen Carothers, asks if anyone has ridden a bull before. One woman raises her hand. "A mechanical one. But not sober," she says, and everyone falls about laughing. Mechanical bulls are a mainstay of some Texan bars.
Predictably, perhaps, there's country music playing while we take turns to try to remain seated while Brutus swivels and jerks beneath us. I manage to stay on for about 20 seconds, which is not embarrassing considering I'm the only British person here, and clearly unaccustomed to this sort of thing.
It's a comfortable 80F (25C) the weekend I visit; wonderful considering this part of Texas had 90 consecutive days over 100F (38C) last year. It's also good considering the next activity I've (perhaps misguidedly) agreed to: the Challenge Course, where my sweat level is guaranteed to rise.
Outfitted in harnesses and hard hats, one by one we're told to climb a rope ladder to a small wooden platform, 30ft high, that towers above the trees. I'm not too fond of heights but the views are stunning. To get from the first platform to the second, however, we must walk across a carved wooden log that looms over the canopy below. Once you reach the second platform, the only way to get to the third is to perform a tightrope walk. I'm clipped on, but by now my palms are sweating and I'm gripping tightly to the rope attached to my harness. The final bit of excitement is the zipline down to the forest floor.
In keeping with the Texas cowboy theme, I head back inside to one of Travaasa's function rooms, where five of us sit on comfy sofas while Michael Rubin, an Austin harmonica guru who has taught the instrument for more than 20 years, relays the basics. It's a bit of a racket to begin with, but in 45 minutes, Michael manages to get us playing some semblance of a tune. All that's missing is the outdoor fire pit and a guitar.
Something cowboys probably didn't enjoy (unless it was in some frontier bordello) is a deep-tissue massage after a long day in the hills. And this is where Travaasa really excels. I opt, naturally, for the "Willie Nelson massage" (make sure you ask for it by its full name), after one of Texas's best-known musical sons.
As "Blue Eyes Crying in the Rain" plays, my legs are covered with a tie-dye sheet and patchouli-and-citrus oil is rubbed into my back. I drift off, and wake some time later to hear Willie covering a Texan classic: "Lone Star, where are you tonight?… It's dark and I think that I would / Give anything / For you to shine down on me."
It's all rather apt, as once my massage is over, I head straight to the outdoor hot tub and sit, under the huge, dark, Texas sky, looking for that lone star.
To fly to Texas, go to Heathrow. Dallas-Fort Worth is served by British Airways (0844 493 0787; ba.com) and its partner American Airlines (0844 499 7300; americanairlines.co.uk). BA also flies to Houston, as does United (0845 607 6760; united.com).
Travaasa, 13500 Farm to Market Road 2769, Austin, Texas (001 512 258 7243; travaasa.com). Doubles start at $450 (£281), including activities such as yoga, guided hiking, the equine encounter, bull fitness and the Challenge Course. Breakfast extra.