The family members, along with their 4-month-old Labrador retriever, were found Sunday morning on the bluffs near Black, Mo., the St. Louis Post-Dispatch reported.
Temperatures had fallen into the 20s and there had been a freezing rain, authorities said.
Reynolds County Coroner Jeff McSpadden pronounced David Decareaux, 36, dead at the scene. His sons, Dominic, 10, and Grant, 8, were transported to a hospital where they were pronounced dead about 2 p.m., officials said.
County Sheriff Tom Volner said David Decareaux, his wife and their five children were in the area for a family trip and to go hiking. On Saturday, Decareaux and the two boys went for a walk and were reported missing after they failed to return home that night.
"When they took off in the morning, it was near 60 degrees," Volner said. "They were last seen by a passer-by at about 2 p.m. [Saturday] on top of Sutton's Bluff. At the time it was raining, and the passer-by asked if they needed a ride. David told the gentleman they could make it back."
An extensive search effort ensued Saturday night, but was called off due to fast-rising creeks and flash flooding.
The search resumed Sunday morning.
"We get lost hikers all the time, but we have never had this happen," Volner said.