01 dodge ram 3500 when 4wd is engaged and making hard L. or R. turn the front end hopes and steering wheel shakes back and fourth had a 99 2500 that one did not act that way any body have any clues All tires are same size and style ??? Oo.
Left: Hey, I got too much traction. You turn.
Right: Eff that, pal. I ain't gonna turn.
You turn!
Left: Up yours! Turn!
Right: Bite me! It's your turn!
If it happens only on dry(-ish) pavement, this is completely expected. But I think you already know that. It's possible that the extra weight of the snow pusher and the salt shaker increase the tire traction, thus exacerbating the condition.
If it happens on slick/snowy surface, you're almost guaranteed to have a failed or failing ujoint. If so, you should also feel the steering wheel shake a little or you might hear the ujoint rattle during sharp turns in 2WD. You should also see significant rust around one or more bearing caps.
With the axles connected fulltime, it is rare to have a ujoint 'freeze' up, since they are always turning (unless the truck sits for months at a time). When they don't always turn, one axis can easily seize, as happened several times on my old F150, dog rest it.
Is the tire pressure correct, and equal?