The Piper PA-12 Super Cruiser propeller plane was reported missing in the area of Tustumena Lake and the Kenai Mountains on Sunday around 10.30pm after it failed to return as scheduled.

But a volunteer pilot spotted the plane on the frozen lake, leading to the passengers’ rescue around 12 hours after the aircraft was declared missing.

“Earlier this morning, a good Samaritan aircraft located the plane wreckage near the eastern side of Tustemena Lake,” the Alaska state troopers said in a statement Monday.

A photo of the partially submerged aircraft published by local media appeared to show three people sitting on the wings.

Rescuers raced to locate the trio in sub-zero temperatures overnight, according to local weather records.

The man and children were taken to hospital with “non-life-threatening injuries”, the statement added.

Dale Eicher, one of several local pilots who joined the search operation, said the passengers were lucky to survive the ordeal.

“I didn’t expect that we would find them and I didn’t expect that we would find them alive, for sure,” he told local TV station KTUU.

“I’ve done a little bit of search and rescue before and it doesn’t always turn out this well.”