Iain Nuttall, 37, from Blackburn, died when the Piper Cherokee flown by his father lost power and hit a tree at the airfield in May 2013.
The Air Accident Investigations Branch (AAIB) said Mr Nuttall might not have been wearing his seatbelt at the time.
Its investigation did not find any mechanical faults with the engine.
Pilot John Nuttall, 61, hired the four-seater plane at Blackpool Airport and took off at 10:30 on 19 May with son Iain and grandson Daniel, five, on board.
Witnesses at Caernarfon told investigators the plane was flying very low, slowly and was making spluttering noises before hitting a tree.
It crashed nose down just inside the airfield boundary, killing Iain Nuttall.
His father and son survived, but both were taken to hospital with serious injuries.
Pilot Mr Nuttall had held a licence since 2006 and was familiar with the route. The report said the weather conditions were suitable for the flight.
But investigators said conditions meant ice could have interfered with the plane's carburetor.
"The investigation did not find any evidence of a failure within the engine but the atmospheric conditions were conducive to carburetor icing," the report said.
The report also stressed the importance of wearing a seatbelt, given Mr Nuttall and his grandson survived.
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Iain Nuttall, 37, was a passenger in a plane flown by his father
Piper PA-28-140 Cherokee (G-ATRR) crashed at Caernarfon airport
PHOTO CREDIT: ARWYN ROBERTS
The trio, all members of the same family, were travelling in the single-engine Piper Cherokee aircraft which crashed on the airfield at Caernarfon Airport, North Wales, shortly before 11.30am yesterday.
A man, who was a passenger in the plane, was cut from the wreckage by fire crews but was pronounced dead at the scene. Two other people were airlifted to Ysbyty Gwynedd hospital in Bangor.
A Welsh Ambulance Service NHS Trust spokesman said a man in his 60s had “serious multiple lower limb injuries” and a young boy had head and abdomen injuries. Their condition last night was described as “critical”.
Police said the three people on board were all members of a family from Lancashire.
A spokesman for the Air Accident Investigation Branch said: “We are aware of the incident and have dispatched a team to carry out a preliminary inspection.”
A spokesman for North Wales Fire and Rescue Service said the aircraft had landed “off the runway” and had flipped over.
Sources at the airport suggested the aircraft, which had been rented from Fly Blackpool, may have clipped some trees close to the boundary of the westerly runway, and flipped over.
Shocked pilots from Blackpool Airport today described the crash as a tragedy and extended their sympathies to the family, who police say are from Lancashire.
Paul Wane, who works at Fly Blackpool, said: “I’m shocked and devastated that one of the aircraft has gone down and it’s been fatal.
“Morale at the airport yesterday was very down, everyone is very upset – it’s a community here.”
Mr Wane, the operations manager at Fly Blackpool, said the route taken by the plane was a “regular” and “picturesque” one flown in what was reportedly an “immaculate” plane. He added: “It’s a picturesque airport ideal for cross country routes.
“The aircraft was immaculate in the hangar on Saturday. It’s tragic.
“Everyone is just wondering why and what went wrong.”
Fly Blackpool CEO Robert Murgatroyd added: “All we can say is our hearts and prayers go out to those involved.”
Airport fire crews were joined by eight appliances from five North Wales Fire Service stations who laid a foam blanket over the area to prevent spilt fuel igniting.
It is not clear what conditions were like at the North Wales airport but flying conditions in Blackpool yesterday were said to be “good”.
Mr Wane added: “Yesterday it was a bit overcast in the morning but I would say good flying conditions, in Blackpool certainly.
“It was one of the best days for flying conditions.”
North Wales Police and the Air Accident Investigation Branch are today continuing their investigations.
Chief Inspector Darren Wareing, from North Wales Police, said: “An investigation is on-going and we are appealing to anyone who witnessed the plane as it approached the runway of Caernarfon Airport to contact police.” A spokesman at the airport in North Wales would not comment on the incident yesterday.
