British event rider Laura Collett will remain under sedation until Friday following her fall on Monday.
The 23-year-old was left seriously ill after the incident at the Tweseldown Horse Trials in Hampshire.
"Laura has had a comfortable night and [is] responding well," said a statement on her official website.
She had regained consciousness on Tuesday after responding well to family at her bedside, with her family keen to praise hospital staff.
The statement added: "She will remain asleep today to aid recovery.
"The nurses and doctors in ICU (intensive care unit) are amazing and Laura is in the best hands.
"Her family and friends continue to be overwhelmed by the support."
Collett, who hopes to compete for Team GB at the 2016 Olympics in Rio, is believed to have suffered lung damage in the fall from the mare Tis A Beauty, as well as some fractures.
She had been training Cheltenham Gold Cup winner Kauto Star for dressage following the record-breaking steeplechaser's retirement last year, and the horse's owner Clive Smith told BBC Wiltshire: "Laura's making good progress and we are hopeful there isn't any brain damage.
"She has got other injuries - some kidney problems - but everyone is optimistic and we hope she gets back in the saddle in due course.
"I could tell when I watched Laura on Kauto Star on Sunday that she is a great rider. She's a lovely girl and we're all hoping for a quick recovery."
Yogi Breisner, Team GB's eventing performance manager, said: "Our thoughts are with her family, friends and everyone in the sport.
"Eventing is a very friendly sport and everyone has been very concerned for her. We hope she makes a full and speedy recovery."
The incident happened days after racing jockey Brian Toomey suffered a life-threatening head injury in a fall. Toomey is in an induced coma in hospital, having had surgery to reduce swelling on his brain following a fall at Perth racecourse last Thursday.
Breisner added: "These incidents in eventing are extremely rare. British eventing has a very good safety record.
"But riding horses can be a dangerous sport and sadly things happen from time to time, however safe it has become over the years."