James Glanton, 34, Christina MacIntee, 25, their two children aged 3 and 4, and a niece and nephew, 10 and 4, were located huddling in a canyon in the Seven Troughs Range.
"They are in pretty good shape," said Pershing County Undersheriff Thomas Bjerke, who participated in the search.
Rescue teams had worked through frigid temperatures as low as 20 below zero for two nights, racing against the elements to rescue the family.
The Pershing County Sheriff's office said they were taken to Pershing County Hospital, but their conditions were not available.
Notable deaths of 2014 [PHOTOS]
Soviets call Reagan joke 'dangerous' [ARCHIVE]