"Four from the group survived and were rescued by helicopter," Sabine Reinthaler, police spokeswoman in Tyrol state, told AFP.
But the others died, with three bodies extracted soon afterwards from the snow and a fourth later after a major search by emergency workers.
"He was recovered around 12 metres (40 feet) below the surface," rescue worker Peter Veider told the Austria Press Agency (APA).
Rescue services said that the victims were believed to be Swiss, APA reported.
The incident occurred near the Jochgrubenkopf peak at 2,450 metres (8,040 feet) above sea level.