Among the dead was the plane's pilot, NBC News reported, citing the Brule County state attorney's office. The three survivors were taken to Sioux Falls for treatment.
Brule County Emergency Manager Katheryn Benton told the Sioux Falls Argus Leader that the victims ranged in ages from 7 to 81.
Three other passengers survived the crash and are being treated at a nearby hospital. Details on their condition were not immediately available.
The FAA said investigators were en route to the crash site and that the National Transportation Safety Board (NTSB) would be in charge of the investigation.
Weather will be among several factors investigators will review, although no cause for the crash has been determined, Knudson said.
It took off from an airport in Chamberlain but crashed at around 12:30 p.m. (1830 GMT) on Saturday.
Brothers Jim and Kirk Hansen founded the Idaho-based company along with their wives, according to Kyäni's website.
"They were our good friends", said Call.
Jim Hansen Sr, his sons, Kirk and Jim Hansen Jr, and six other family members died when their plane went down in a field near Chamberlain, South Dakota, according to relatives. The American Meteorological Institute had forecast gusty snowfalls that "could significantly reduce visibility".
The area is under a severe winter storm warning with heavy blowing snow or freezing rain. Local authorities were guarding the site on Sunday, he said.
At least nine members of a family from Idaho, including two children, returned from a hunting weekend, were killed when their single-engine aircraft crashed into a field of fire.
The Federal Aviation Administration also has been notified, according to Maule Rossow.
Maule praised first responders as "heroic".