It took off from an airport in Chamberlain but crashed at around 12:30 p.m. (1830 GMT) on Saturday.
Twelve people were on the aircraft and among the dead are the pilot and two children, according to Brule County State Attorney Theresa Maule.
The three survivors were transported to Sioux Falls for treatment, Rossow said. Three others were injured.
The National Transportation Safety Board said three investigators were stranded in Sioux Falls, about 140 km east of the site.
Knudson told the Associated Press weather will be among several factors that the agency will investigate, but said it was too early to determine.
The accident happened on early Saturday afternoon when the aircraft, a single-engine Pilatus PC-12, took off from Chamberlain Municipal Airport for a flight to Idaho.
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The Hansen were active in the community of Idaho Falls and Jim Sr., along with his sons, held prominent positions within The Church of Jesus Christ of Latter-day Saints.
A group of Idaho Falls residents were killed today when their small plane crashed in South Dakota.
"They were our good friends", Name stated. They were not bright, but silent, important contributors. The Weather Service cautioned of ice, snow and winds as fast as 40 miles per hour as bad weather across the country was predicted to hit millions of travelers returning home after Thanksgiving. Local authorities were guarding the site on Sunday, he said.
Rossow also said that first responders and medical professionals worked to rescue the victims in "extreme weather conditions".
The number of people who died in plane crashes spiked in 2018, according to a new report.