A man who was lost in the mountains along with his three children for three days during a snowstorm said he was terrified they wouldn't make it out alive, but he remained strong for his children and relied on his faith.

Frederick Dominguez and the children, who vanished while looking for a Christmas tree, were rescued Wednesday by a helicopter from a snowy ravine, just as another storm was bearing down in the foothill region about 100 miles north of Sacramento.

"You just want your kids to be safe and you're just praying, `God, keep my kids alive,"' Dominguez told reporters at Feather River Hospital in Paradise.

The rescue came as relatives and friends were starting to lose hope. One snowstorm had covered the family's tracks, and an even bigger storm was hours away from burying the four even deeper.

"I'm just amazed how well they did," Lisa Sams said after seeing her children and ex-husband for the first time since they went missing. "It was like butterflies in my stomach, like if you were going to go on a very first date."

The four appeared to be in good shape as they bounded from a California Highway Patrol helicopter that ferried them to safety in two trips; Alexis, 15, and Joshua, 12, were taken out of the woods first. Their 38-year-old father smiled at cheering relatives and friends later as he and his 18-year-old son, Christopher, emerged from the aircraft.

They were taken to the hospital and checked for dehydration, hypothermia and frostbite, physician Kurt Bower said. They were released within hours, but early Thursday, Alexis was readmitted for pain in her toes from minor frostbite.

Michelle Nye, a spokeswoman for Feather River Hospital in Paradise, said Alexis was admitted to the hospital shortly after 2 a.m.

After he had been checked at the hospital, Dominguez described three harrowing nights in the wild as he tried to keep his children from panicking and succumbing to the numbing cold. Joshua needed constant reassurance.

"I said, `Son, I would tell you what I bought you for Christmas if I thought we weren't going to make it,"' Dominguez recalled. "My kids were relying on me, and I'm scared, but you can't tell them you're scared."

The ordeal began Sunday, when Dominguez and the children left church and headed to the mountains to cut a tree for Christmas. Because the father had custody of his children at the time, his ex-wife did not know they were missing until she learned Joshua failed to show up at school Monday.

By the time authorities learned they were missing and began their search Monday night, the first storm had dumped 8 inches of snow around the family's parked pickup truck, obliterating its tracks. The family went missing about 25 miles northeast of Chico, near the hamlet of Inskip.

By Wednesday, the storm had dumped more than a foot of snow in the mountains, leaving wind-driven drifts 7 feet high in some areas.

The family members— found less than a mile and a half from the road — said they got lost by going from pine tree to pine tree, trying to find the perfect Christmas tree, until they realized they were lost.

"I just remember walking and walking and thinking, `We're not going to make it.' I remember being really, really scared," Alexis told CNN Wednesday night.

They eventually wandered into a culvert that allowed a creek to flow beneath a dirt road, and stayed there until their rescue. It was a miserable place — dark, cramped, wet and cold — but provided just enough shelter.

One night it rained, sending snow melt shooting through the tunnel. At one point, Alexis lost a shoe and slept a night with her foot exposed. Dominguez ripped his sweat shirt and tied the shreds around her foot, rubbing it to keep it warm.

Outside, they used twigs and branches to create an SOS — "Help."

They used humor and songs from church to lift their spirits.

The breakthrough in the search came mid-afternoon Wednesday when the highway patrol helicopter spotted the father atop a small bridge and landed nearby, sinking into 2 feet of snow. Dominguez said he ran across rocks and snow in his bare feet when Alexis heard the helicopter.

Cloud cover had prevented an aerial search until a brief lifting of the clouds.

Flight officer David White said it was the last opportunity for the chopper, and that snow was falling heavily as it descended.

"With another storm coming in, they were just happy to get out of there and get home," he said. "It's probably the best Christmas ever."

Dominguez moved to the rural foothill town of Paradise about a year ago from Los Angeles to be closer to his children, who live with Sams.

He joked that next Christmas, he'll buy a plastic tree.