Under glowering skies, the Dominguez family set out Sunday afternoon to find the perfect Christmas tree. A couple of hours after church, darkness would fall -- but they knew this spot in the mountains, just a half-hour away, where the woods were thick and a million perfect Christmas trees beckoned just off the road.

After three nights of snowstorms and subfreezing temperatures, they were rescued Wednesday when a California Highway Patrol helicopter pilot saw "HELP" spelled out in tree branches on the snow.

The family's search for the perfect Christmas tree had ended, but their hopes for the perfect Christmas -- which is to say, any Christmas -- came alive.

"It was just a relief," said the father, 38-year-old Frederick Dominguez, a Los Angeles native who hadn't been in the snow since he was 12. "It was, 'Man! Lord! You saw us through!' "

Dominguez and his three children had spent bitterly cold nights huddled in a culvert, but doctors at the Feather River Hospital in Paradise described them as in remarkably good condition Wednesday afternoon.

All were treated for frostbite before they were discharged Wednesday night. Still, they were eating heartily and preparing for their close-up on national TV.

Lisa Sams, the children's mother and Dominguez's ex-wife, said her daughter was excited about her sudden chance to be on TV, but asked: "Do I get to shower first?"

Sams, who has lived in Paradise for five years, told reporters at a news conference after the rescue that she was "overwhelmed with just joy."

After Sams reported her ex-husband and her children -- Christopher, 18, Alexis, 15, and Joshua, 12 -- missing Monday, the community rallied in their support. To discourage untrained volunteers who might get lost, the Butte County Sheriff's Office had to block a road to the search site. After the rescue, a local radio station announced that it would give the family the very thing that triggered their ordeal: a Christmas tree.

Dominguez and the children headed into the hills in a pickup about 3 p.m. Sunday, parking about a mile north of an old mining settlement called Inskip, off a narrow mountain road called Skyway. Although it wasn't snowing when they got out of the truck, night would soon fall and a storm would blow in, disorienting the family even more.

At a hospital news conference, Dominguez described how the family went uphill, cut down a tree with a battery-operated saw and started back downhill. But they never found the road they expected and, as darkness fell after a two-hour march, they realized they would have to spend the night outdoors.

By the light of their otherwise inoperable cellphones, the four fashioned a lean-to out of tree limbs. Winds howled through it as the storm slammed in. Dominguez said he didn't sleep that night, nor did his oldest son. Each tried to block an open end of the crude structure, shielding the younger children between them.

By Tuesday, daughter Alexis was complaining that one of her toes had gone black. Dominguez and his children tucked one another's feet inside their shirts to warm them.

"You go into survival mode," Dominguez said. "Any parent would do that."

A religious man, he said he prayed "for a cave or a shelter, for God to help us." The four found a wide culvert beneath a fire road and stayed there the next two nights, passing the time with songs and shared fantasies of places they would like to go to eat.

"The only food we had was in our thoughts," said Dominguez, a pest-control employee who moved to Paradise in March to be closer to his children.

The four were dressed in light jackets, sweat shirts and sneakers.

"Next time I go out there, I won't be a knucklehead," Dominguez said. "I'll have some boots on."

His son Christopher told CNN that the family camps out during the summer, but wryly added: "The way we go camping isn't like what we did over the last few days."