At 2380m, the cave is close to The Lizard, a line of rock high up near the summit, near the entrance to the Crater Valley.
"It might have been adequate, for a short time and in better conditions ..." Mr Smith says as his voice trails off.
The conditions have been atrocious. Mr Smith and some of his team, him grey with fatigue and his hands still not fully functioning, ponder at how she could have lasted so long.
"I have never been in worse conditions on the mountain," says one of his colleagues, who won't be named, and doesn't really want to be quoted, because Smith's their leader and it's up to him to tell it.
The tough men, some sporting Hillary-like beards and that lean stance, are shocked when they look at themselves coming down the mountain in the half light to the search headquarters.
"Everyone was just covered in ice, it was hanging off us," said Mr Smith.
He is exhausted as he tells his story yesterday afternoon in the sunny warmth of the North Egmont Visitor Centre.
He's been up for days. He was halfway through a DVD, Terminator number something or other, unwinding from the previous all nighter, when he got the call. There's been no real sleep since. More than 30 people were crammed into Tahurangi Lodge, 1520m up on a ridge, on Sunday night - climbers and alpine experts from all over the island, who came to help.
Smith and eight others, teams one and two combined, left the lodge at 12.30am yesterday, armed with headlights, crampons, ice axes - all the gear. They saw little: "Visibility was down to between three and five metres."
They climbed up Hongi's Track and up into Snow Valley, where the winds were gusting at "only" 80kmh.
At 2100 metres - Mr Smith's GPS was still working - they traversed to the leeward side of The Lizard, its eastern flank, where there was a bit of shelter from the freezing westerly.
From there, they started to make it safe for team three, who would follow to try to make contact with the stranded pair.
Mr Smith and crew got 2200m up the side of the Lizard, then crossed over its top to 2272m, just 50 metres from the Crater Valley. There, they were hit by the full force of the wind, the 100kmh stuff, that started literally to freeze them.
The ground they were clinging to was covered in hard rime, which they described as ice laid over more ice, building in formations. Ice axe territory, one in each hand.
Sensing danger of the dreaded kind, Mr Smith turned them around.
On the way down, they met the next group, briefed them on what to expect.
The also meet Gerardo Cuervo. Mr Gerardo, from Spain, was climbing solo and heading for the top, when they met about 2000m up.
He was in the middle of telling them how they could safely get down when he was informed, politely, that perhaps it's best if he turned back. He did, willingly: "Very bad conditions up there," he said as he emerged from the summit track at midday.
He was not the only one to think the mountain is a pushover. On Sunday evening, as a police crew member headed away from the North Egmont carpark, he was met by a French couple in a van.
"We want to climb zer mountain," said one. "Um, not a great idea tonight," said the policeman. "But we are very experienced." Policeman: "The forecast looks better for tomorrow."
Mollified, they drove away. Perhaps put off by yesterday's continued cloud cover, and maybe by news of the unfolding tragedy, they didn't turn up again.
It's something Darren Morris, a member of the Ruapehu Alpine Rescue Organisation, said he was familiar with. One of Vaughan Smith's advance team, Mr Morris said easy access to Mt Taranaki was no different from that at Mt Ruapehu and the other central North Island mountains, where people were often caught out by sudden changes in weather.
"That's one of the problems, I guess. They promote the mountains as places where anyone can visit, so people just do it."
His colleague, Stu Arnold, a 22-year veteran of alpine rescues who came from the Ruapehu area to help, said conditions on Mt Taranaki early yesterday were among the worst he had seen.
"Nil visibility, 100 kilometres an hour gusts, snow blowing off the summit. It wasn't quite a blizzard, because it wasn't snowing, but it was pretty tough going," said Mr Arnold, one of 18 from the Ruapehu area who arrived to assist on Sunday.
Many of the rescuers -from RARO, the Ruapehu Ski Patrol, the Sir Edmund Hillary Outdoor Pursuits Centre and the Department of Conservation - were all unpaid volunteers.
Why do they do it?
"I'd like to think someone would come out after me if I got into trouble. Simple as that, really," said Darren Morris one of Mr Smith's advance team members.
Not so simple was the realisation they all carried away from the mountain, that despite their extraordinary efforts, this was a mission without a happy ending.
