The child, named as Matthew Young, died after being crushed by a horse at Kypehall Farm in Lesmahagow, South Lanarkshire.
It is understood he was waiting to ride the horse when it stumbled and fell on him in front of his mother, Margaret.
Matthew, four, suffered serious injuries and was taken by ambulance to nearby Wishaw General, but died a short time later.
The youngster is believed to be the nephew of top showjumper Alex Barr, and the accident happened on his farm.
Last night people on an equestrian social website spoke of their shock at the news of Matthew's death last Thursday.
One woman wrote: "Really heartbreaking for Alex Barr and his family. Alex is a well known rider and producer of sport horses. My thoughts and prayer are with Alex and his family at this tragic time."
She added: "We're all pretty shocked up here. Alex and his sister - Matthew's mum - are regular competitors. A lovely family. Just awful and heart breaking."
Another poster, Jacqui Broderick, wrote: "Such a terrible tragedy - a freak accident, but such a horrible consequence."
Police said the death was not being treated as suspicious.
A Police Scotland spokeswoman said: "A postmortem examination will be held in due course to establish the exact cause of death. However, the death is not being treated as suspicious."