like what parts? is that what your asking for?
I would say as much as you can and this isnt for only "mudding" but any use that not easy driving on pavement.
inspect tie-rods and ball joints (oil them)
brakes (no one likes seized brakes)
look for any loose or dangling lines (oil) (brake) (Radiator) (no bueno)
if you can grease your shocks do it (some can)
ive never heard of greasing due to of road specific activities just perform general maintenance and its fine.