What to do with "Antarctic Guide" and "Dog Sled" while playing against an Ancient One from the base game?
As long as you are playing with the Antarctica side board, those cards are usable.

From the expansion rules, page 2:


  When playing with the Mountains of Madness expansion, add
  all expansion components to their respective decks or pools
  of Eldritch Horror components except for the components
  described below.
  
  [unrelated items skipped]
  
  Shuffle all Unique Assets to create the Unique Asset deck.
  Place this deck faceup near the Asset deck.