Australian man Michael Bishop, 53, and German father and son Johann and Raphael Viellehner, aged 58 and 27 respectively, were last seen on Linda Glacier on Monday morning.
Police said two helicopters had been searching the area this morning in vain and it was believed the trio perished on the mountain.
"The situation is grim," police said.
"It was hoped that if they had survived the storm they would have been spotted from the air today."
The three men's families had been advised that they were probably dead.
Further aerial searchers would take place over the next few days to find their bodies. The Christchurch based search and rescue team had returned home and Department of Conservation searchers were on standby.
About 30cm of snow had fallen at Plateau Hut, where the trio had set out from on Monday.
Senior Constable Brent Swanson said they were expecting the worst.
"If they were up and moving we would have seen them today.
The final helicopter sweep was happening this morning as it flew back to Christchurch with volunteers, he said.
Department of Conservation Mt Cook Search and Rescue team leader Jim Spencer said they had flown above the terrain this morning searching for signs of life.
" We flew above because it provides higher visibility ... we were looking for anything out of the ordinary, splashes of colour, movement, anything that was unusual."
Swanson said the area would continue to be monitored and there was a number of operators in the area who were also keeping a "look out".
Raphael Viellehner, a 27-year-old german, is one of the three climbers missing on Mt Cook.
Chief guide Dave McKinley said searcher were disappointed with the news, and people in Aoraki/Mt Cook village were "feeling for the family members of the people involved".
McKinley, who took part in the search, said New Year's Eve and New Year's Day had historically been "very bad days" on the mountain, as they fell in peak climbing season.
If the climbers are confirmed dead, the number of deaths on the mountain would total 238.
Department of Conservation summer mountaineer Stu Haslett was the last person to die on the mountain after falling on December 13.
CLIMBERS 'EXTREMELY FIT'
Raphael Viellehner is a talented runner and has completed numerous competitive races.
Johann Viellehner had significant climbing experience and had climbed in parts of Europe, including Russia.
Bishop had previously climbed peaks in the Aoraki/Mt Cook National Park.
Bishop is understood to be a GP in Brookvale, Sydney.
Staff at his former clinic described him as an avid climber. They knew he was on holiday, but they did not know where.
Thanks to - The Press for permission to run this article and to Stuff for permission to use the two photos of climbers.