His brother witnessed the fall and had to spend the night in a hut before rescuers could reach him.
The victim was still alive when rescuers reached him, Helicopter Line pilot Jim Campbell told the Herald on Sunday.
``He was very badly hurt and he'd lost his hat and gloves in the fall so he was very cold.''
The rescue team had to carry the man by stretcher down a glacier, walking two hours to reach a rescue helicopter.
A Westpac Rescue Helicopter from Christchurch was called to help with search and rescue co-ordination at the Mt Cook base. By the time it arrived, the man had been transported to Mt Cook Village by a local helicopter service and had been pronounced dead by paramedics.
He had been planning a four-day ski tour of the area and was using the Tasman Saddle Hut as a base, police said.
Mr Campbell said police told him the man was well-equipped but was not wearing crampons when he slipped.
A massive rescue bid was made shortly after 11am on Friday, with members of the Aoraki Mt Cook Department of Conservation Alpine Rescue Team, Alpine Guides, The Helicopter Line, Twizel and Fairlie police and Westpac Rescue paramedics all called in to help.
Constable Joseph Rush, of Twizel police, said the weather conditions were severe, with poor visibility, strong wind gusts and -15C temperatures.
The man's name will not be released until family have been notified.
- additional reporting by Cherie Howie