The pair made it to a remote hut on the mountain on Tuesday and raised the alarm with the Department of Conservation (Doc).
It is understood they may have frostbite, but an alpine rescue crew is in touch with them and continuing to assess their conditions.
The pair are said to have enough food and water for an extended stay.
Bianca Bratton from the Mountain Safety Council is not involved in the rescue, but is well aware of the challenging terrain.
"It goes without saying that these areas up in our high alpine are some of the country's most remote and wild environments, so they are particularly volatile," she told RNZ's Checkpoint programme today.
"The search and rescue team is going up against some really crazy weather systems that continue to sort of hamper their efforts in the region."
The climbers were in the best place by staying at the hut, she said.
Rescuers are hoping the weather clears so the pair can be flown out.
"At the moment it's not possible to get a team in on foot, so they'll be waiting for a clearance to get the helicopter to fly in and take the pair out."
The Doc huts "definitely don't have your creature comforts," Bratton said, with no shower, comfortable couch or wifi.
But they do have radios and climbers in these kind of environments typically carry satellite phones or other reliable communication devices, so they have been in touch with rescuers.
"Most critically, the huts do provide a refuge for climbers like these people from the snow and the wind and they do provide a small amount of insulation from the cold."
The climbers were well prepared for their adventure, Bratton said.
"They really should have food to get them through to the next break in the weather.
"These routes to and from the huts are really only appropriate for experienced mountaineers so I hope that they are equipped, and it sounds as though they've got everything they need to wait it out until rescue is a possibility."
Spring conditions can be highly volatile in the Aoraki/Mount Cook area and recent weather has been very unpredictable across the Southern Alps.
"I know that new snow is predicted over these new couple of days."
Frostbite is a big risk in cold temperatures, Bratton said. It can affect the fingers, toes, nose or other extremities.
"The good thing is they're in touch with their search and rescue team. They do have medical advice to help them treat it in the interim.
"It's not clear at the moment exactly how serious their frostbite is."
