Leacock said the group were well prepared and equipped for a great day out in the mountains, when one member of the party sustained an uncontrolled slide above the Tukino ski field.
Police said the woman was in a nine-strong group climbing the eastern side of the peak, traversing the Cathedral Rocks around noon on Saturday when she fell.
One of her companions climbed down to be with her while help came but strong winds meant helicopters were unable to reach her, with search and rescue teams taking to the slopes by foot to reach them more than five hours later.
Leacock said the group had good communications and were able to contact search and rescue immediately.
The injured climber and the rest of the group were helped off the mountain by the rescue team.
Unfortunately, the injured member was pronounced dead at Tukino Lodge, she said.
The New Zealand Alpine Club thanked the Ruapehu Alpine Rescue team, search and rescuers, police and the public for their efforts in getting the party safely off the mountain.
The club's thoughts were with the family of the dead climber, and also those involved in the trip and the rescue.
Leacock said it was a difficult time for them and the climbing community in general.