But the family defied amazing odds, and was found Tuesday, safe and sound, in a remote, snowy area of southwestern Oregon. Their chances of survival were so bleak that searchers had given up looking for them, CBS News correspondent Vince Gonzales reports.
They survived, along with the family dog and cat, in their snowbound recreational vehicle by rationing dehydrated food and other provisions.
Their trip started as a vacation. Six members of the Hill-Stivers family — Pete Stivers, 29, Marlo Hill-Stivers, 31, their children Sabastyan, 9, and Gabrayell, 8, and Stiver's mother and stepfather, Elbert and Becky Higginbotham — began a short journey in an RV more than two weeks ago.
The group left Ashland, Ore., on March 4, setting out across the mountains to the coast, which normally takes a couple of hours. A relative reported them missing March 8, and a desperate search began.
Two adults were found after they left the RV, which had gotten stuck in snow, to seek help. Hours later, rescuers found the others and they were reunited in Glendale, about 80 miles north of the California border.
Later, Peter Stivers and Marlo Hill-Stivers ran up to a van as it pulled into town with the two children and Stivers' mother and stepfather, Becky and Elbert Higginbotham of Arizona.
"I love you baby," Marlo Hill-Stivers told her daughter, Gabrayell, 8.
"I love you too, mommy," she replied.
Peter Stivers rested his hands on the shoulders of his 9-year-old son, Sabastyan.
"He had fun. They enjoyed it," Peter Stivers said. "They didn't know we was in trouble."
"Since I've been so good, my dad's going to buy me a rocket," Sebastian told The Early Show.
Still, for the adults — and their worried loved ones — it clearly was an ordeal.
As Peter Stivers explained to the The Early Show, the family was driving when they "took a wrong turn and we got stuck and we was like, OK, we'll dig out a little bit." But as they dug out, the got stuck again, Stivers said.
"We were cold, we could see our breath ... I was trying not to break down. I'd hide my heads under the blanket and cry a little bit but not let anyone see me," Marlo Hill-Stivers told The Early Show.
They were lost, and ultimately got stuck in about 4 feet of snow, at about 3,800 feet, on a dicey mountain road.
"We thought we'd take the scenic route," said Elbert Higginbotham. "Every time we took a corner, it seemed like we took a wrong corner."
At one point, the RV slid off the road. The family tried to hand-dig the RV out but could not.
Elbert Higginbotham says the family sustained itself on snow and dehydrated food they had loaded for the trip. They had enough propane to keep the RV heated.
Police Chief Rick Mendenhall of Shady Cove, Ore., who helped in the rescue, told The Early Show co-anchor Julie Chen that they had about an eighth of a tank of gas left and about a quarter of a tank of propane left when he reached them.
"But they were all in real good spirits," Mendenhall said. "Their mental status was all good. They were pretty happy to see me. All their vital signs were within normal limits."