Steering box grease - manual steering

If you are adding grease to a box but not cleaning it out fully you need to use the same type of grease that is already in the box to prevent the compounds in the grease from causing damage if they interact badly. The OEM also has a lower dropping point than most greases, that means it does not take much heat to soften it up in the winter so it flows and lets the steering loosen up. Many common moly lubes are higher so they would steer stiff for longer.
The factory grease is sold as Ford XG-1-C and is a molybdenum based grease light grease. Can be found in many places online or at a dealer.

If it has never been touched but is not having a real problem I would turn the wheel to one side fully. Then pull the fill plug and remove one of the cap bolts and just pump in new grease until you see it come out the bolt hole, then turn the wheel the other way and add some more. Reinstall the bolt and plug and drive it. I would not tear it apart unless you plan on a full rebuild, in which case it would be a lot easier to just replace the box with a rebuilt unit as it is easy to get the pre-load and side plate settings a bit tight or loose and cause the box to wear faster.