My recollection in researching this a decade ago was that the cold weather made the behavior of the rudder change (my term was invert, maybe that’s not accurate), and pilots were trying to pull up, but in fact putting the plane deeper into a nosedive. Some 25 seconds later they hit the ground at some 300-400 MPH and vaporized.
The only way to have saved the plane would have been to dump the hydraulics and/or switch to a manual fly by wire mode, neither of which were a logici thing to do in the 15 seconds they had to save the flight.
I’ve only flown for 20 hours in a Cessna so sorry if my terminology isn’t perfect!