As stated, cable lube is usually the problem. When the lube gets stiff, the needle starts wagging the dog. If you were in the south, I would agree with soft grease. Instead, use speedometer cable lube, it contains a lot of graphite and doesn't get as stiff when it's cold. You can get it at an auto parts store.
You can remove the cable from the housing by disconnecting the housing at the tranny. Carefully grasp the end with pliers and pull. When you put it back in you need to turn it so the square drive will slip back into the speedometer head.
I usually go ahead and replace the cable and housing. Don't know if you can still buy the kit locally for your truck. They also sell a generic cable that you cut to fit and crimp on an end. Last one I bought had lube with the new cable.
