A trailer and tractor backed into Harry Whitlam at Swithens Farm, Rothwell, West Yorkshire, on 9 August 2013. He died later the same day.
Leeds Coroners' Court heard Harry was struck at an area of the farm not usually open to the public.
Tractor driver Gary Green was arrested but never charged.
Mr Green had 90 micrograms of alcohol in 100ml of breath at the time of the accident. The legal limit is 35 micrograms.
The court heard Mr Green was arrested on suspicion of drink-driving and causing death by dangerous driving but was later released and never charged.
West Yorkshire Police said a criminal prosecution could not be brought because the incident occurred on private land.
Jurors were told Harry had gone into the area where he was run over just after 09:00 BST.
His mother, Pamela Whitlam, who worked at the farm's cafe, said she had not explained to him where he could or could not go because she was not familiar with the layout of the site.
In a statement to the court, she described how just before the accident she told her son: "Be careful."
Moments later she ran outside to find him lying on the floor after being hit by the vehicle.
Jurors heard Mr Green had drunk "three of four pints" at the pub the night before the accident and continued drinking at home until 01:45.
Following his arrest, he told police officers: "I don't know where he came from because no-one should be down the back of the tractor."
The inquest continues.
Update 31 July 2015: This story has been amended following updated information supplied by West Yorkshire Police about why a prosecution could not be brought.

Several publications suggested last week that the president-elect would offer the star a top job in the arts.
In a statement, Stallone said he was "incredibly flattered to have been suggested to be involved with the National Endowment for the Arts (NEA)".
But the star said he would prefer to highlight issues faced by US veterans.
"I believe I could be more effective by bringing national attention to returning military personnel in an effort to find gainful employment, suitable housing and financial assistance these heroes respectfully deserve," the statement said.
Stallone, famed for his role in the Rambo and Rocky films, is also an artist.
He has created hundreds of artworks and last year exhibited at the Modern Art Museum in Nice, France.
In 2013, a collection of his paintings went on display at The Russian Museum in St Petersburg.
At the show's opening the star said, if he had the choice, he would spend his life drawing instead of acting.
"I think I'm a much better painter than an actor," he said.
The Oscar-nominated actor studied art before his film career took off.
In an interview with Variety earlier this year, Stallone said: "I love Donald Trump. He's a great Dickensian character. You know what I mean? There are certain people like Arnold [Schwarzenegger], Babe Ruth, that are bigger than life. But I don't know how that translates to running the world."
Established in 1965, the NEA is an independent federal agency which distributes government grants to arts organisations.
The NEA has come under threat in the past from previous Republican governments, including Ronald Reagan's administration.
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A tractor driver was almost three times the legal alcohol limit when he reversed into an 11-year-old boy, an inquest has heard.
[NEXT_CONCEPT]
Actor Sylvester Stallone has said he is "flattered" by reports that Donald Trump may offer him an arts post - but would prefer a role helping veterans.