So, just to be clear, this is a "I canna doooo it, Captain! We dooona have th' poooer!" kind of a shimmy, right?
The only thing that I can think of is maybe if your wheels aren't on tight enough, or your tires are out of balance.
Are your wheels packed with snow? That will throw things into a wicked shimmy at all speeds.
Does your truck have Idler arms? If yes, are they worn out? We had a big van that developed that issue. It pulled to the right when you slammed on the brakes. Anything like that?
Is it stuck in 4WD and doing the "Crab Walk"?
Are your tires old and misshapen?
I'm sure that I can think of other things to check, but I am drawing a blank right now.
