The first time I saw the elk was from a ski bus. The driver shouted over his shoulder, and we all leaned to the left and pressed our noses against the windows. But all I could see was a flat pasture several miles wide, unbroken white but for a swath of dark mud.

"Where are they?" I asked the driver.

"Right there," he said.

"How many?" I asked, straining to see a few females or, if I was lucky, a majestically antlered bull.

"Do you want me to stop and count them?" the driver asked dourly. "About seven or eight thousand."

The "mud," it turned out, was actually the elk, the thousands that make up Jackson Hole's winter herd, gathered tightly together. Every year these second-largest members of the deer family (only moose are bigger) descend from their summer ranges in Yellowstone National Park, Bridger-Teton National Forest, Targhee National Forest and unprotected wilderness areas to the more than 24,000 acres that make up the National Elk Refuge in Wyoming's Jackson Hole. The refuge's herd has been growing. Last winter, more than 9,000 elk were counted on the land in and adjacent to the refuge; 7,500 is the target herd size.

I had come to Jackson on business and had intended to spend my leisure time on the ski slopes. But, captivated by that vision on the ski bus, I made time to visit the elk refuge, just a half-mile from the town square on Broadway.

In the early 1900s, the grazing areas of the elk in this part of western Wyoming were being diminished as ranchers fenced off land to raise cattle. During the harsh winters of 1909, 1910 and 1911, thousands of elk died of starvation, and the survival of the herd was threatened. In 1912, the National Elk Refuge was created to provide protected grazing areas for the elk as well as lands where they could be fed when the grass was buried beneath deep snow and ice.

Access to the refuge is extremely limited, but 45-minute sleigh rides set out from the visitors center during the months the elk are wintering here -- mid-December through March.

The day I visited, the temperature was about 25 degrees, the air crisp and clear. About 20 of us boarded an old wooden sleigh-wagon, pulled by a pair of Clydesdale horses, for our ride. The horses jerked forward, and we set off across the ice field in silence.

Suddenly, there they were. We approached the herd at a fair pace, but the elk paid little attention to our arrival. Most of the animals rested placidly on their knobby legs, or stood still, turning their heads as we passed; a few young males butted heads but dispersed as we got closer.

Each time we thought we'd seen the largest elk ever, someone would point ahead to one even larger, the driver would pull us closer, and we'd gasp in admiration at the way the old bulls could hold their heads so high and nobly despite their heavy racks. The animals can lose as much as 100 pounds during the winter. Even so, mature cows in winter weigh about 500 pounds, bulls about 600 or 700 pounds.

We circled the herd, picking up elk facts as we rode. Contrary to popular belief, we learned, you can't determine the age of an elk from the number of antler points -- although you can get a pretty good idea. Young bulls between 1 and 2 years old have short, unbranched antlers called spikes; the next year, antlers usually have three or four points on each side. Older bulls with six points on each side are called royal bulls; those with seven points on each side are called imperial bulls.

However, all bulls, no matter what their ages, shed their antlers every spring, usually in March and April. Local Boy Scout troops gather the antlers each year to sell at a public auction in the Jackson town square. Held the third Saturday in May, the annual event attracts buyers from all over the world.

We flooded our guide with questions. He pointed at the fat ravens picking at the carcass of an elk that had died of sickness or old age; then he pointed to the hill behind us, where three small, brownish bumps were barely visible in the distance.

"Coyotes," he said. "They're too nervous to get close to the herd now, but once the elk shift away from the carcasses, they'll be moving in."

As we slid along, I noticed long, dark green stains in the snow. Our guide explained that they were the remains of that morning's supplemental feeding of alfalfa pellets, which are deposited in long lines behind a sled in the mid-mornings.

The elk receive supplemental food for about two months during the most severe winter weather, when forage is scarce. Even then, however, the alfalfa feedings account for less than half of the elks' winter food consumption.

The best elk-observing coincides nicely with the ski season. If you can stand the cold -- and you probably can if you're in Jackson Hole to ski -- January and February are the best months to visit the refuge.

By March, the herd has grown smaller and less impressive, as the elk leave in small groups for their summer pastures.

We stopped one more time to take pictures of an especially large, old elk, and then began to travel the mile or so back to the visitors center.

It had started to snow lightly, and the shadows were long.

The National Elk Refuge offers 45-minute sleigh rides continuously from 10 a.m. to 4 p.m. daily, mid-December through April 1. The cost is $6 for adults, $3 for children 6 to 12; free for children under 6. For more information, contact the National Elk Refuge, P.O. Box C, Jackson, Wyo. 83001, (307) 733-9212. Anthony Newman is a writer in Brookeville, Md.