The remaining climbers still missing were identified as Anthony Vietti, 24, of Longview, Wash., and Katti Nolan, 29, of Portland.
A search was set to resume at dawn for Vietti and Nolan.
"This is still a rescue operation," Strovink said, adding that family members had been notified and some had joined rescue crews.
Strovink declined to give any details about the remaining climbers but said all three were experienced and well-equipped.
Mount Hood, the tallest mountain in Oregon, is a popular site among climbers in the United States. In 25 years, it has been the site of dozens of climbing accidents and fatalities.
The worst on record happened in May 1986 when nine people -- seven students from Oregon Episcopal School and two adults -- died after they dug a snow cave during a sudden storm.
The latest search comes almost exactly three years after another trio of experienced climbers died on Mount Hood during a December 2006 blizzard.
The three reported missing Friday did not have a radio locator beacon but they did have a cell phone that was briefly activated about 1:30 a.m. Friday as the climbers were leaving Timberline Lodge to begin their ascent, Strovink said.
The trio reported missing Friday left Timberline Lodge on Mount Hood about 1 a.m. that day and failed to return by afternoon.
Strovink said the trio were making a technical ascent of the west side of the 11,249-foot volcano near Reid Glacier.
The glacier ranges in elevation from about 6,000 feet to 9,800 feet. The upper extent of the glacier is known for crevasses.
Gullberg's body was found at about the 9,000-foot level, Strovink said. He did not say whether the cell phone was found with the body.
Steve Rollins of Portland Mountain Rescue said a locator beacon would have been helpful in this case but many rescuers oppose a mandate to carry them because they believe it will lead some climbers to take risks they otherwise would avoid.
"And that increases the risks to rescuers," he said.
Rollins noted that climbers often receive good signals on their cell phones on areas of the mountain but the phones sometimes lack enough power to send out a call or message.
"It's frustrating believe me," Rollins said, "when you can see all the way to Salem or beyond and wonder how many cell tower sites are out there."
Strovink said about 30 searchers focused on the area around Reid Glacier.
He described weather conditions on the mountain as "cold, icy and treacherous."
National Weather Service forecasts called for slightly warming temperatures on Sunday with snowfall tapering off.