COLORADO SPRINGS, Colo. — Here’s the thing about Western art. Like rattlesnake steaks and Rocky Mountain oysters, it’s an acquired taste. If your great-grandparents crossed the mountains in a covered wagon or homesteaded west of the Missouri River, it could be in your genes.

But when a friend from Connecticut scoffed at the genre’s two most famous artists, Frederic Remington and Charlie Russell, dismissing paintings of cowboys and Indians as “just poster art, best painted on black velvet,” I dared him to take the “immersion cure.”

“Join me for a couple of days at Cloud Camp, on Cheyenne Mountain in Colorado Springs,” I told him. “I’ve been there. You’ll be surprised.” What I didn’t mention was that Cloud Camp, one of three backcountry camps connected to the Broadmoor Hotel, in Colorado Springs (www.broadmoor.com/cloud-camp), was owned by billionaire Philip Anschutz, a Western enthusiast. Or that cowboy and Indian paintings were part of the theme at both places.

At Cloud Camp, where paintings and North American native artifacts are displayed in every room, all the guests — whoever they are, willing or not — are exposed to a double-dose of what AI (artificial intelligence) scientists call “deep learning.”

Simply put, this is the ability to recognize individuals in a particular group — dogs, faces, airplanes, or in this case, Western paintings — because you’ve seen so many of them. Deep learning is why trained robots can distinguish between a human face and last month’s Halloween pumpkin.

Agreeing to a date, and the terms of the bet — a spa treatment for the winner — we booked a couple of nights at Cloud Camp and a couple at the Broadmoor. Then we bought tickets, flew to Colorado Springs and checked in with staffer Hannah Brenneman, at the Broadmoor’s Base Camp reservations desk.

Spotting a familiar-looking painting behind the desk, and two more in the hallway, I mentioned it to Brenneman, telling her I thought I’d seen it somewhere. Could it have been in a museum?

“You could have,” she said. “Or it could be a copy, though I don’t know for sure. There are a number of copies in our collection, but nobody knows which ones they are. You’ll see some up at Cloud Camp, but they don’t know either. And here’s your shuttle,” she added, escorting us to the door. “It’s seven winding miles, with 12 steep switchbacks to the top. Enjoy the views!”

Before “taking the cure,” we decided to tour the Lodge, a monumental chinked-log chalet worthy of a small Tudor castle. Wedged between weathered boulders and a pine and spruce forest, at a breezy 9,200 feet, the building is supported by giant logs so long and broad they had to be carried up the mountain one by one.

The views from the rear deck outside took my breath away, with the valley below and Pikes Peak to the north, its bald summit rising above timberline. It’s that rare sort of view you get only from the top of another mountain.

Inside the Lodge, the Great Hall soared to the ceiling, 24 feet at the highest point. Rows and rows of windows and 20-foot walls offered enough space and light for the paintings, as well as Navajo rugs, buckskin clothes, a saddle, leather chaps, antique spurs and a stuffed black bear.

Dark-stained beams, two big fireplaces, sofas and chairs and a banqueting table set for 26 announced that this was the gathering place. And it was here, in the Great Hall, where it sank in: we were at the heart of what might be the single largest collection of Western art ever displayed on a mountain top.

The paintings, vertical and horizontal canvases in gold frames, were everywhere, hanging between and over the windows, above the doors, in the halls, over the fireplaces and near the ceiling.

Following a detailed printed guide, we wandered from one painting to the next, comparing Remington to Russell, and both of them to Henry Farny, Charles Schreyvogel, Joseph Sharp, Walter Ufert, Ralph McGrew and others.

A couple of them new to me. And my friend, now three-quarters of the way toward losing our bet, confessed that he hadn’t expected such painterly skills, such skillfully rendered shadows, and so many different scenes and subjects. “You could tell the history of the West through art alone,” he said.

After that, with the argument nearly settled, we put on our hiking boots and headed for the closest trail. And like most visitors to Cloud Camp, we crammed in most of the activities, from a guided archery lesson, a mule ride and a cooking clinic (with the chef). Horseshow contests and corn-hole games with other guests filled in the gaps.

But it was the evenings, with sunsets over the horizon, the three-course dinners, the inventive recipes and fresh ingredients and the other guests, convivial new acquaintances, that won me over.

“This is a special place,” said Julie Fuller, seated next to me, explaining that it was her eighth visit to Cloud Camp. “My husband, David, surprises me by organizing it every year. Up here on the mountain we’re above it all, down there. It makes you feel as if you’ve left your troubles behind.”

The Fullers, traveling with family, said that one of their group had tried the zip line, 10 separate double cables, ranging from 200 to 1,800 feet long. Connected by short hikes, it included two perilously swaying suspension bridges. And for those with a taste for fright, you could finish with a 180-foot long “horribly, excitingly, scary rappel down to the Seven Falls.” Next time, I said, wishing I’d tried it sooner.

If you want to include tennis or golf, spend your last couple of days at the hotel, on the expansive Broadmoor “campus,” at the foot of Cheyenne Mountain. You can take a paddle boat out on the lake, work out in the lap pool or sign up for fishing lessons. There’s a bowling alley, a movie theater, a half-dozen pubs serving craft beers and at least eight different restaurants.

If time allows, consider buying a ticket to visit the Seven Falls, which rush downhill in a nearby box canyon. But you won’t see both the falls and the pools between them, unless you’re willing to climb up 224 steps installed along the side walls. Once a scenic pearl, lauded on many a sepia-toned postcard, the Seven Falls have become a commercial attraction. So I passed it up, and collected my winnings instead: a more than satisfying massage.

If you haven’t already overdosed on paintings, there are plenty more in the Broadmoor’s three wings: 150 more, to be exact. We’re saving them for next time.

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(Anne Z. Cooke, a would-be painter, gets her kicks at museums.)