Jockey George Baker is awake in intensive care in a Swiss hospital after a fall during a race at St Moritz on Sunday.
Baker was riding Boomerang Bob on the frozen lake track when the horse was brought down and fatally injured.
Baker was taken to hospital and the remainder of the meeting was abandoned.
"George has woken up, and with the hospital releasing the news I can only imagine they are pleased with his progress," said his agent Guy Jewell.
"He's already had a CT scan and that has come back clear.
"They will obviously need to check that everything is working properly and his wife is on her way out there."
Racing has taken place for decades on the frozen lake at St Moritz, with horses fitted with special shoes to cope with the wintry conditions.
Race organiser White Turf said a crack was found in the ice when the track was checked after Baker's fall.
It added: "This meant that water had come up to undermine the racetrack."
Oxfordshire-based Baker, who is 6ft tall, won the world's oldest classic, the St Leger, last September on Harbour Law.
His fellow jockey Christophe Soumillon, who was also riding at St Moritz, told French news agency Equidia: "Turning into the straight, the snow was only up to the horses' shoes.
"You could see by the prints afterwards that there was water between the ice and the snow."