The men were long-lined one at a time off the mountain by The Helicopter Line, Aoraki Mt Cook Rescue Team and Alpine guides to a safe area at Plateau Hut, before being flown to the emergency services building at Mt Cook village, police said.
"Police urge anyone who is heading to the high country or Southern Alps over the long weekend to ensure that they check the weather forecast, tell someone of their intentions and carry appropriate equipment for all kinds of weather," a police spokeswoman said.
"In the remote areas of the Southern Alps a personal locator beacon is invaluable if you need to raise the alarm in the event of an emergency."
Dave McKinley, chief guide at Mt Cook Alpine Guides, said Mt Tasman was known as "the mountaineers' peak".
"It's a long and involved climb on mostly snow and ice," he said.
The usual route was via the West Coast side from Pioneer Hut.
"You would expect the round trip to take up to 15 or 20 hours."
The north ridge was the standard route from the western side, and it had been the scene of several rescues in previous years.
The weather in the national park was beautiful today, he said.
"It's a lovely day in the mountains," he said.
"You could expect quite warm, soft snow due to the storm we had about two days ago, so I would expect it to be beautiful weather but potentially soft conditions, [which] would slow you down."
