Q: Once a Keeper has been found in the “Expotition” and declared The North Pole, does it still count towards any of the Goals that use it?

…For example, if it were the Piglet card, could it no longer be used to win with a goal that required Piglet?

A: “The North Pole” is a title or honorific which is added to something’s name, rather than replacing or negating it. Just because Piglet is The North Pole, doesn’t mean he’s not still Piglet.