Mt Cook had been missing climber's Christmas wish

Stormy conditions on Mt Cook have hampered the search for the three missing men.

On Christmas Day, Australian climber Mike Bishop decided he'd finally summit the mountain that previously eluded him.

The doctor and pastor from Sydney is missing on Aoraki-Mt Cook, along with father-and-son German climbers Johann and Raphael Viellehner.

The trio left Plateau Hut at 1.30am on Monday to climb to the summit of the mountain via the Linda Glacier route. They were last seen at 4am at Teichlemann's Corner on Linda Glacier. They had been due back on Monday afternoon.

Atrocious weather has thwarted the search for the three men this week but rescuers are confident conditions will improve enough today to start searching again.

Dr Bishop's eldest son Joshua said from Sydney that the family took comfort from an outpouring of support.

Dr Bishop's friends and family gathered last night to pray for the three missing men.

Dr Bishop, 53, started climbing as a medical student some 30 years ago. On two previous trips to New Zealand, he'd had to turn back from Mt Cook after nearing the summit, Joshua Bishop said.

"Cook's something he's really wanted to do. On Christmas Day, he was like: This is it. We've got a good period of weather coming up and this will be the time to do it."

Missing climber Mike Bishop. His son said he was an experienced climber and would have gone out prepared. Photo / Supplied

Dr Bishop hadn't planned to climb with the Viellehners but after meeting them they had decided to summit together.

Joshua believed the three met at Plateau Hut.

Joshua was confident his dad was prepared but said an injury among any of the three could complicate efforts to find shelter.

"He's very safe ... He goes out there with the right gear. He doesn't go unprepared.

"One time he got caught in a big snowstorm and he had to make an igloo, or a snow cave, and he did it and survived and came back with all his limbs and fingers ... so he did the right job.

Joshua said it was good the three men were together, combining different kinds of expertise.

He believed Johann Viellehner, 58, had climbing experience in cold parts of Russia. Raphael Viellehner was 27, the same age as Joshua.

"I have complete confidence the three of them would have put their heads together and said: Let's find a cave, let's make something to stay warm."

Joshua said the efforts of authorities and volunteers in New Zealand were heartening.