Showjumper Emily Gilruth suffered a 'traumatic brain injury' after falling from her horse during the Badminton Horse Trials.
Mrs Gilruth, from Threapwood in Malpas, is under sedation at Southmead Hospital in Bristol.
The 40-year-old was injured after she fell from her mount Topwood Beau at the third fence of the cross country course on Saturday (May 6).
Doctors have been 'pleased' with her medical progress so far.
A statement was issued on behalf of her family today (May 8).
It said: "Emily's family would like to thank all the many well-wishers for the lovely supportive messages they have received.
“The doctors are pleased with her progress. She has had a stable night and remains under sedation.
“We would like to say a huge thank you to Badminton’s medical team, for their efficient and very caring service, also to the staff in the Intensive Care Unit at Southmead."
Mrs Gilruth, who is married with two daughters, has been eventing for 18 years.
She had been 'in the running' to join the British equestrian team ahead at the London 2012 Olympics.
Her dream was shattered when her horse Splash was taken away from her by its owner, starting a legal battle from which she was eventually paid £60,000 compensation in 2015.
This was Mrs Gilruth's second year at the Badminton Horse Trials after she made her debut in 2016.
Her horse, a 14-year-old gelding, was uninjured in the fall, which happened at the Keepers Question obstacle.