How was the "frozen wing flap grease" problem solved? (Antarctica, 2001 emergency evac)
Flying with the flaps extended is perfectly possible, just inefficient. At that point they were probably just trying to get in the air, not worrying about their fuel efficiency or airborne speed. Otters normally land and take off with flaps somewhat extended. The main problem is that with flaps fully extended, acceleration will be low, so it will be a long, slow takeoff. One issue is that if the plane has any icing, being in a full-flap condition can lead to a stall.

Once things get down to -50F or below, stuff really starts to freeze. For conditions like that you need to start replacing grease with graphite lubricants. Even fuel freezes so the planes have to use special heaters.

Here is a more technical description of the event by an electrician:


  We then refilled the smudge pots and brought out tanks containing
  about 1,000 gallons of fuel to refuel the plane. They also brought out
  3 Herman-nelsons, portable diesel heaters used to warm up planes and
  other big equipment. At about 2:15AM, the plane was started but some
  of the hydraulics in the tail controlling the flaps were frozen. We
  called to get the Herman-nelsons back to heat up the flaps. They ran
  their engines the whole time, and we had to bring out another 100 or
  200 gallons of fuel.
  
  Finally, at about 5:00 AM, the plane was working right and was ready
  to go. But then it appeared the plane was stuck in the snow. So a
  couple of guys stood on a car-like vehicle with tank treads, and shook
  the plane's wing. This caused the whole plane to rock back and forth.
  But finally the plane broke free and taxied to the skyway. The plane
  turned around and took off and flew in the -64F air.
  
  Brother Aaron Coy, Local 48 Portland, OR Amundsen-Scott South Pole
  Station, South Pole, Antarctica


There are no hydraulics in the tail, obviously, so the electrician is confused about something. The hydraulic system in an ski-equipped Otter is used for the flaperons (in the wing) and for the ski controls.



Twin Otter at Casey Station