CONCORD, N.H. — Olga Box told friends she wanted an adventure during her family’s February school vacation.

So the Box family decided to spend two nights in a bare-bones cabin on Mount Cardigan in western New Hampshire, where they’d have to hike to the cabin and bring everything with them, including extra wood for the fire and water to drink.

The adventure turned into a nightmare when the 43-year-old Groton woman and two of her children became lost on the trails Tuesday night.

By 10 p.m., when Box and her children, Olivia, 13, and Zachary, 11, didn’t show up at a designated spot and a search by other family members yielded nothing, the New Hampshire Fish and Game Department was notified.

Box and her two younger children had been hiking with her husband, Jeff, and their older son. Their plan was to hike the two miles from the Appalachian Mountain Club’s Mount Cardigan Lodge to the club’s High Cabin, where they had planned to spend the night. The cabin is about a half-mile from the summit of the 3,100-foot mountain.

Shortly after 5 p.m., the three separated from the others in their group and went ahead to reach the cabin. They took a wrong turn at an intersection and then became “disoriented and confused,” according to Fish and Game Lt. Todd Bogardus.

They eventually took shelter in an abandoned, unheated camper they found and holed up for the night as temperatures dipped to the single digits.

Fish and Game Conservation Officers, the Upper Valley Wilderness Response Team and Appalachian Mountain Club workers searched the mountain trails.

At 1:45 a.m. yesterday, with clear skies and temperatures in the teens, Conservation Officers Bradley Morse and Jeremy Hawkes located the three, safe and uninjured, in the camper alongside the Woodland Trail.

The family was about 1 1/2 miles off their planned course.

They then hiked the group back out to be reunited with the rest of their family, who had left High Cabin and returned to the trailhead at Mount Cardigan Lodge, where the family is staying until they return home. The family could not be reached for comment last night.

Although the group did have sleeping bags, maps and other winter-hiking overnight gear, “this incident should remind hikers of the importance of following the hike-safe principle: When hiking as a group, stay as a group,” Bogardus said. “Had they done so, this incident could have been avoided.”

Scott Carpenter, of the Upper Valley Wilderness Response Team, said four members of his team were involved in the search. He said the family had left a backpack and a pair of snowshoes to mark the trail entrance for rescuers to see.

Although the family did many things correctly, they made a critical mistake in not staying together.

“It was a biggie,” Carpenter said.

Jan Hurst, owner of the Clover Farms Market in Groton, employs Olga Box and considers her a friend. Hurst said the family is athletic, and love to hike and cross-country ski.

She described Box as someone who is “very calm and level-headed. … If I was going to be lost with anybody, I’d want it to be her.”

Hurst said she is anxious for Box, who she describes as an exceptional baker, to return to work on Monday to talk about her adventure over homemade cookies.

Said Carpenter: “There are lots of searches that don’t have happy endings. This was one of the better ones.”