To your point, traditional 4x4s can be bad in on-road type snow. I know you know this but nerding out more for others, we're full time 4WD with the center diff. Important as that let's each tire track individually. When we lock the center, that makes us equivalent to 4x4. In this mode, it can force slipping of tires, particularly in turns. For those that remember back in grade school, sliding friction can be considerably lower than static friction, which is why unlocked is advantageous in this type of use.
Airing down incrementally can also help find more traction on-road.