Furgler is one of Austria's most popular mountains, but most people
approach it from the east. From the north the path is rather exposed but not technical, rather less busy and somewhat shielded from the hot sun.
Following that, we can pass three or possibly four 2500m+ lakes, and
then summit the Witch's Head, Hexenkopf. Finally, we descend back to
See.
Note that the path turns right (signed Klettergarten) shortly after Ascherhütte, otherwise you will end up going up to Glockspitze (on a path not marked on the Hiking Buddies map), dropping down to Furglersee, and adding 4 km and 3.5 km to the route.
This route starts from the valley in See. Alternatively, we could save 5 km each way, and 730 m ascent and descent, by taking the Medrigjochbahn (€12 up,
€7 down, or €13.50 combined, I presume only in one day). Given
the limited hours of operation, I think that making the last cable car
down is almost impossible in one day, but the route could be split in
two at the Hexenseehütte (€9 for young DAV members) or Ascherhütte (€10
for young DAV members).