Nice pics of the 2006 Tucker.
Here is what R J would say:
1) That isn't that bad, everyone at Togwotee in the grooming operation has seen worse if they have been there for more then a season, no question about that.
2) That model and all Tuckers will start with decent batteries easily at -10 to -15 below without so much has hesitation if it's running synthetic oil and the operator allows the grid heater to come on and let it do it's thing two or three times shutting off the key and recycling the system before turing the key to start. No need to leave it idle really.
3) A chain or snatch block and another cat would have pulled that out without too much hassle, especially when the stuck cat is driveable. The drag would almost certain need to be disconnected though and dealt with later.
4) The Terra snow tracks have MORE (proven) traction (when tested in all conditions) then it's comparable steel cleat brother when comparring apples to apples. Remember folks, Togwotee's steel cleat cats of years past were 38" wide tracks and the tracks you see in the photo's are 26" or 28" depending on the manufacture of the track (camoplast or Tayeruk respectively). It takes an entirely different approach to driving a Terra track then a steel track that is for certain.
5) As for not seeing the groomers going out? WTF, unless you ride from 5pm to 5am you more then likely won't see them out at all. There hasn't been a time that I have been out there that at least one of the cats wasn't filling up at the station at 430pm ready to go out for the evening. Trust me, I pay attention to these things. It has to be a very special occasion that something isn't at least attempted to be groomed nightly.
Since I'm not out at Togwotee day in and day out it's tough for me to say but why it always seem to leave a cat stuck in the back country for more then 24 hours is beyond me. Maybe it was weather (which it probably was) but anything else (mechanical aside) if they would have enough guys to do all the tasks around there it would be a simple daylight recovery and all would be well. Just seems a lot of the time is there is not enough people to do all the jobs out there.