Eaton Tru-Trac differential

i guess there was absolutely no resistance to turning felt at the snow wheel side.
The spring loaded nature of a clutch or cone diff might have helped there.
i.e one of them would still work a bit, depending on the spring loading with 1 back wheel off the ground
the trutrack won't because it needs feedback via some resistance to turning from both wheels in order for the various internal parts to "ride up the appropriate ramp" (wrong term i know to do with gear pitch....eeerrrr ) to do the biasing...

looks like you discovered the failure scenario.

Dave