Owyhee County Sheriff Daryl Crandall said the survivors of the crash were in "surprisingly good condition" after the plane went down southeast of Silver City, KTVB-TV, Boise, Idaho, reported.
The Idaho Transportation Department said the 1966 Cessna 172 took off from Sacramento and was en route to Mountain Home, Idaho.
One of those who had been aboard the plane called 911 and reached the Owyhee County Sheriff's Office early Sunday.
Rescue workers aboard air ambulances had a hard time seeing in the darkness early Sunday and Crandall said ground crews had to turn back because of blizzard-like conditions. Responders encountered snow drifts as high as 6 feet and steep terrain.
Once responders reached the survivors, they wrapped them in blankets and built a fire while awaiting an airlift.
The Idaho Army National Guard UH-72 used a hoist to reach the survivors one at a time. They were taken to Saint Alphonsus Regional Medical Center in Boise.
Authorities identified the three survivors as Brian Brown of Wilton, Calif., his wife, Jayann Brown, and their daughter, Heather. The person who called 911 told police one of those who had been aboard the plane had minor head injuries and cuts and two others suffered back and neck injuries.