David Coulthard, who raced against Schumacher for 13 years, backed his friend to "come through the greatest challenge of his life" as former drivers and Angela Merkel, the German Chancellor, sent messages of support.
Schumacher had ignored advice to skiers to stay on the pistes in the resort of Meribel, where he owns a chalet, after heavy snow increased the risk of avalanches and obscured rocks.
He hit the right side of his head and Jean-Francois Payen, chief anaesthetist at the Grenoble University Hospital Centre where Schumacher was being treated, said his helmet "protected him in part" from the violence of the impact, adding: "Someone who hadn't been wearing a helmet would not have got here. Despite the helmet he has serious lesions [injuries]." He added: "It is too early, at this stage, to make a judgment about the future of Michael Schumacher. His situation is critical."
He said Schumacher had had emergency surgery after arriving at the hospital to remove blood from a haematoma, or bleeding inside the brain, and there were no plans for a second operation. The haematoma caused swelling in a critical location in the brain.
Professor Stephan Chabardes, the neurosurgeon who operated on him, said: "The next 24 hours are critical. We monitor developments. The next 24 or 48 hours will be decisive."
Schumacher's body was being kept at a temperature of 34C to 35C, below normal, to reduce the brain's need for oxygen. Doctors said he was in "an artificial coma and a state of hypothermia".
Schumacher was skiing with his 14-year-old-son, Michael jnr, when he fell.