But they became separated in the afternoon and Mr Dowall failed to reach the hut.
Mr Hawes stayed there for three nights, but this morning was flown out by helicopter as weather conditions in the area are fine today, after days of strong wind, rain and heavy snow.
A search and rescue operation began on Thursday night and Mid-South Canterbury police area commander Inspector Dave Gaskin said searchers scanned the mountainside for the missing climber.
"The search commenced between 5.30 and 6 this morning, at first light at Mt Cook.
"This is a big open area of snow and ice... So far there is no sign of [Mr Dowall] or any sign of where he's been. With two or three days of really poor weather, any tracks he left would be pretty much gone."
Mr Gaskin said there were a lot of crevasses in the search area and these were areas of interest.
They were also, however, making it too dangerous to send rescuers in by foot.
After today's flybys of the area, a hold has been placed on the search for now. It looked unlikely the helicopter would go up tomorrow, as the weather closed in again.
The search would be re-assessed on Tuesday.
"Really what we're waiting for is to see if the snow that's fallen melts."
Mr Hawes was now in the village and had been able to help rescuers pinpoint where his missing mate might have been.
"He's obviously extremely worried and concerned about his friend. Apart from that he's perfectly fine," Mr Gaskin said.
Mr Dowall's distraught wife Sovann last night said she was desperate for her husband to return and she hadn't sleep or eaten since she learned he was missing.
"I miss him so much, I need him, what can I do without him?" she told the Herald on Sunday.