Marian Clode, 61, was on an Easter break in Northumberland with her two grandchildren, husband, daughter and son-in-law, when a cow charged at her and attacked her three times.
She died days later in hospital in April 2016, having suffered a severe spinal cord injury in the fall.
Farmer Alistair Nixon, 62, on behalf of the JM Nixon partnership which runs Swinhoe Farm, near Belford, appeared at Newcastle Crown Court to plead guilty to a health and safety breach.
He admitted failing to ensure the safety of persons other than employees by exposing them to risks to their safety from the movement of cattle.
Craig Hassall KC, prosecuting, said the farmer and employees were moving a herd of about 140 cattle from winter quarters to summer grazing, using a public right of way from the 1,700 acre, mixed farm to a field.
Mr Nixon was positioned by a quad bike at the head of the bridleway and used a stick to stop some of the cattle from moving down the path before he was ready.
But a group of seven or eight cows and five or six calves got past and headed off along the bridleway and over the brow of a hill, out of sight, but along the enclosed lane.
Mrs Clode and her family, who were staying in holiday cottages on the farm and who had been out for an afternoon walk, were coming in the opposite direction.
Other family members managed to get out of the way by leaping over a barbed wire fence but Mrs Clode was attacked by a cow which turned 90 degrees towards her as she stood by a wooden gate.
Mr Hassall said: “It charged at her two or three times and then tossed her over the wooden gate.”
Her son-in-law managed to get into the field where she lay unresponsive and face down and the emergency services were called.
Mr Nixon arrived at the scene and assisted with first aid, the court heard.
The teacher was taken to Newcastle’s Royal Victoria Infirmary where she died from her injuries.
Mr Hassall referred to a statement by Miriam Parker, a cattle behaviour expert, who said farmers were guided by the Highway Code when moving livestock and they should be kept under control on public rights of way at all times.
The court heard Mr Nixon had travelled on his quad bike along the route he intended to use to move the cows, but that was some time before Mrs Clode and her family were on it.
Mr Hassall, referring to Miss Parker’s expertise, said: “Cattle in full-blown fight mode will attack using their head, often repeatedly, and patently that is what transpired here.”
He said cows being moved with their calves would exhibit “higher arousal levels” on a spectrum of anxiety, excitement and fear.
Even older cattle being moved from their winter sheds to open field can become more excited, play-fighting, prancing and bucking, he said.
The cattle behaviour expert said several issues could have made the cow react as it did, including a fear of falling if it was being forced quickly downhill by more dominant animals behind.
Judge Tim Gittins said whether it was a single factor or a combination was not clear, adding: “Something did trigger the fight reaction.”
Mr Hassall replied: “They are all reasons that might contribute in these particular circumstances to a particular cow going into fight mode rather than flight mode.”
The prosecution said the defendant had not made a “suitable and sufficient” assessment of the risk of moving cattle down the public right of way.
Tom Gent, for the defendant partnership, said the business employed “experienced and competent” stockmen.
Mr Nixon did not keep aggressive or over-protective cattle and had got rid of such animals in the past, the firm’s barrister said.
Mr Nixon grew up on the farm and knowledge had been passed on from his father and grandfather, Mr Gent said, and workers were well aware that cows could behave more protectively when their calves were with them.
He believed the cattle that bolted would stop to graze on their way to the field, and he did not immediately follow them on his quad bike.
Mr Gent said: “Of course, with the benefit of hindsight, that is something he bitterly, bitterly regrets.”
Judge Gittins will pass sentence at 10am on Friday.
Mrs Clode was born in Londonderry and lived in Ashton-under-Lyne, Greater Manchester.
