Joshua Dominguez, second from left, and Alexis Dominguez, third from left, are helped by authorities after they were flown by helicopter to Sterling City, Calif., on Wednesday. The Dominguez family vanished Sunday on a Christmas tree-cutting trip in the northern California mountains and were found alive Wednesday after huddling in a culvert for warmth during three days of heavy snow.

Paradise, Calif. ? A father and three children who vanished on a Christmas tree-cutting trip in the Northern California mountains were found alive Wednesday after huddling in a culvert for warmth during three days of heavy snow.

A California Highway Patrol helicopter crew spotted Frederick Dominguez waving his arms atop a small bridge and landed nearby, sinking into 2 feet of snow, flight officer David White said. White said the crew found the family on their last pass over the area as snow from another storm, even bigger than the first, started to fall heavily.

“Our hearts are all full right now,” said Cory Stahl, who closed his pest control business so his employees could help look for Dominguez, an employee. “It’s a very merry Christmas now.”

The helicopter ferried the family to safety in two trips; Alexis, 15, and Joshua, 12, were taken out of the woods first. Dominguez, 38, smiled at cheering family and friends as he and 18-year-old Christopher emerged from the helicopter a short time later.

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

All four were talking and drinking hot chocolate while being checked at Feather River Hospital for dehydration, hypothermia and frostbite, treating physician Kurt Bower said. They were all released from the hospital later in the day.

“I’m surprised how good they are,” he said. “There’s a miracle from God in there somewhere.”

The family survived wearing only jeans, sweat shirts and coats and by huddling in a culvert beneath a bridge, sheltered from the outside by twigs and tree branches. They had written “help” in the snow with branches.

The youngest children were pushed deepest into the shelter, with the father and eldest son blocking the wind, Sams recounted after visiting with them at the hospital.

She said they told of huddling together, telling jokes and singing songs to pass the time in the first couple days, before beginning to grow scared and depressed in the last 24 hours.

They found water to drink but did not eat snow because their father remembered reading that it could cause hypothermia.

Frederick also had taken off his sweat shirt, torn up the fabric and wrapped it around his children’s feet, hoping to stave off frostbite. Alexis’ toes were changing color, Sams said, but Frederick kept rubbing them to try to keep them warm. Color began to return to the girl’s toes in the hospital.

Dominguez and his children had been missing since Sunday in the region about 100 miles north of Sacramento. Dominguez’s pickup truck was found Monday night parked along a mountain road some 25 miles northeast of Chico, near the hamlet of Inskip.

The family – 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, before realizing they were lost.

“My daughter goes, ‘Mom, you know how we are. We get excited, and we see a tree and then we see another tree,'” Sams said. “They just got lost, and they ended up taking a side road that led them to the opposite direction.”