Two women and one man tumbled 30 metres on the mountain Sunday, and their dog -- a black Labrador named Velvet -- jumped after them.
"The dog probably saved their lives" by keep them warm during the night, Erik Brom, a member of the Portland Mountain Rescue team, told The Associated Press.
A team of about 30 people, battling blowing snow and ferocious winds, rescued the climbers Monday.
"Their condition is very good at this time," Russell Gubele, who is co-ordinating communications for the rescue operation, told CNN.
"They were located in the area where their mountain locator units suggested that they were, and we finally got some of our rescuers down there to them. They are fine. They are being warmed up right now and fed by our rescuers."
The climbers were well-equipped and had been in cellphone contact with authorities.
Gubele, of Mount Wave Search and Rescue, said despite their fall, the climbers said they were not badly injured.
They were found huddling with Velvet, inside sleeping bags and under a tarp to keep warm. Rescuers told them to eat as much food as they could and stay in place until they were located.
But winds gusting to 110 km/h and blowing snow made it tough for rescuers to get to them.
Some of the rescuers took shelter behind rocks overnight in the White River Canyon, and waited until daybreak to continue their search because of the treacherous conditions.
Rescuers hoped to get the three out before another storm, expecting to bring up to 40 cm of snow, hit on Monday.
The three climbers should be able to walk out. A rescue vehicle would be sent to pick them up, Gubele said.
Five of eight climbers were brought down from the mountain Sunday night.
The drama began when the team of eight climbers set out on Saturday, camped out overnight and began their descent on Sunday afternoon. At the 8,300-foot level, three of the lead climbers slipped and fell off a ledge.
At least one of the climbers was carrying a device that sent out signals, and Gubele said it helped rescuers pinpoint their location.
Mount Hood can be treacherous, particularly in the winter. In December, search teams scoured Mount Hood for days in the hopes of finding a group of missing climbers alive.
The bodies of Brian Hall, of Dallas, and Jerry "Nikko" Cooke, of New York, have not been found. Another climber in their group, Kelly James, of Dallas, died of hypothermia.
In the past 25 years, more than 35 climbers have died on the 11,239-foot mountain, one of the most frequently climbed mountains in the world.
With files from The Associated Press
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