Carwyn was on holiday with his family when he is believed to have asked to ski alone on the final run of the day.
French police said he fell 160ft (49m) to his death after leaving the piste.
The Foreign Office said the accident happened in Flaine, 38 miles north west of Chamonix, on Friday.
The family run a small farm and rent out a number of luxury holiday cottages.
Relatives, who were looking after guests and tending the animals while the family was away, were too upset to speak.
Carwyn was reported missing at 16:30 local time and his body was found at the bottom of a 100-metre cliff at 19:00 local time.
Michel Ollagnon, police commander for the nearby town of Bonneville, said the boy fell after apparently losing his way.
He had been skiing with his mother, brother and sister.
Mr Ollagnon told the BBC: "It seems as if the boy did the last piste descent of the day on his own after asking his parents' permission.
"He appears to have become lost before falling over the edge of the cliff after taking his skis off.
"A helicopter was deployed in the search before his body was recovered.
"A judicial inquiry into what happened has begun."
The Foreign Office said it was providing consular assistance to the family.
A seven-year-old boy who fell to his death on a skiing holiday in the French Alps has been named locally as Carwyn Scott-Howell from the village of Talybont-on-Usk, near Brecon.