Airline spokesman Ed Martelle said Flight 2253 from Chicago "had a long rollout" when it landed at 11:37 a.m. Wednesday. The plane came to rest on a hard surface and did not go off into grass or brush, he said.
There were 175 passengers, two pilots and four flight attendants on board the Boeing 757, Martelle said.
"There was snow everywhere outside the windows. We couldn't see anything. But there was no big impact," Kevin Huelsmann, a local newspaper reporter who was on the flight, told The Associated Press. "It happened so quickly, most people didn't react until it was over."
He said the pilot told passengers after the plane had come to a stop that the brakes had failed.
Ray Bishop, director of the Jackson Hole Airport, said Wednesday that there were no injuries and no damage to the airplane, which he said went into deep snow 658 feet past the end of the runway. That distance included a 300-foot paved safety apron and 358 feet (110 meters) of dirt beyond that.
Light snow was falling when the plane landed, with visibility at about 1.5 miles, Bishop said. The runway had some snowy patches, but its surface afforded good braking friction, he said.
Martelle said airline officials were trying to determine why the plane went off the runway.
The National Transportation Safety Board announced Wednesday it has opened an investigation into the incident.
The National Weather Service said Jackson Hole had received about 7 inches of snow after midnight.
Airport officials plowed around the plane and brought stairs to the aircraft so passengers could exit.
Buses were sent out to the end of the runway, reports CBS affliate KIDK.
Crews used bulldozers to pull the airliner back onto the runway.
The airport's only runway is 6,400 feet long, which Bishop said is a little shorter than normal for airports handling commercial flights. Another airplane went off the end of the runway last month, and such events happen periodically there, he said.