The small plane, a Pilatus PC-12, took off at around 12:30 p.m. local time at the Chamberlain Municipal Airport for Idaho Falls, Idaho.
Three survivors managed to escape the wreckage and were taken to nearby hospitals. At least nine people were killed, including children, and three others are believed to have survived.
The Brule County Sheriff's Office is investigating the crash, alongside the FAA and the National Transportation Safety Board.
Knudson said the plane was bound for Idaho Falls, Idaho, and crashed within a mile after takeoff on Saturday.
Brule County will not be releasing the names of those in the aircraft until all family members have been notified.
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.
Family friends said the two businessmen were on a Thanksgiving hunting trip in South Dakota and were coming back home.
The area is under a severe winter storm warning with heavy blowing snow or freezing rain. They were not bright, but silent, important contributors. The American Meteorological Institute had forecast gusty snowfalls that "could significantly reduce visibility". 12 people were on board the single-engine plane.
Maule praised first responders as "heroic".
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