New Orleans —David Decareaux Jr. and his two young sons loved to go hiking, and the boys, Grant, 8, and Dominic, 10, were eager to make a day hike on the Ozark Trail while on a family vacation in southeastern Missouri, David Decareaux Sr. of Madisonville said Tuesday.

That outing ended in tragedy Saturday when the three got caught in a sudden change in the weather, Decareaux Sr. said. The three were found on the trail by searchers Sunday morning, victims of hypothermia. The father was dead at the scene; the boys were taken to a hospital where, after hours of efforts to save them, they were declared dead.

The lone survivor, the family’s Labrador retriever, was found near the bodies of the boys, their grandfather said tearfully, “trying to keep them warm.’’

The younger Decareaux, 36, was a native of New Orleans, who moved with his parents, David and Carmen Decareaux, to the North Shore when he was 12. He graduated from St. Paul’s School in Covington in 1994 and attended LSU for two years before joining the Air Force in 1997.

While stationed at Scott Air Force Base, he met his future wife, Sarah. After their marriage, they lived all over the world — The Azores, England and Naples among other places — before settling in Millstadt, Ill., in October with their five children. Decareaux had retired from the Air Force and was working as a project manager at Scott Air Force Base, his father said.

The camping trip to Brushy Creek Lodge in Reynolds County, Mo., was to celebrate the couple’s wedding anniversary.

“He had surprised her with a camping trip,which they’d done often,’’ his father said.

The family enjoyed the outdoors. “They loved to go hiking with their dad,’’ Decareaux said of his grandsons, and the two older boys had been eager to go on the outing Saturday, he said.

When the three didn’t return by 4 p.m., Decareaux said, his daughter-in-law, Sarah Decareaux, raised the alarm. She had stayed behind at the lodge with their other children, Katie, 12, Finn, 4, and Elise, 2.

More than 50 volunteers set out to search, some on horseback, but worsening weather conditions forced them to suspend the effort after midnight, Decareaux said. The hikers were found Sunday morning.

It was nearly 60 degrees Saturday morning when the three set out on the popular trail that runs through a sparsely populated area of southeast Missouri. Reynolds County Sheriff Tom Volner said that Decareaux was wearing only a light jacket, while one of his sons was clad in a fleece pullover and the other a sweater. They were ill-equipped as the temperature sank into the 40s, and a storm that would drop 2 inches of rain set in, making the trail all but impassable.

The temperature eventually dipped into the upper 20s.

Volner said there are no caves or other places of refuge along the trail. Although Decareaux had a cellphone and flashlight with him, both devices lost power at some point, Sarah Decareaux told the St. Louis Post-Dispatch on Monday.

A passer-by spotted the hikers more than three hours into their journey and asked if they needed a ride back to the lodge, but Decareaux declined, telling the man they could make it back, Volner said.

The sheriff said that the hikers missed their turn back to the lodge.

“By that time, their light played out. You don’t have any ambient light down here because there are no cities or towns. When it’s dark you can’t see the back of your hand,” the sheriff said.

The tragedy crushed Decareaux’s father-in-law, Keith Hartrum, who described the family as tightly knit, “always on the go and adventurous.”

“Dave was a great guy, a good father, son-in-law and husband,” Keith Hartrum said. “Those two boys were just precious — smart, very nice kids.”

Funeral services are scheduled Friday morning at Quernheim Funeral Home in Waterloo, Ill., with internment at Jefferson Barracks National Cemetery in St. Louis with full military honors, David Decareaux Sr. said.

The Associated Press contributed to this story.

This story was updated on Jan. 16, 2013 to correct Carmen Decareaux’s first name.