The ability that defines Barrowgoyf's power and toughness counts card types, not cards. If the only card in all graveyards is a single artifact creature card, Barrowgoyf will be a 2/3. If the cards in all graveyards are ten artifact cards and ten creature cards, Barrowgoyf will still be a 2/3.

Card types that can appear on cards in a graveyard are artifact, battle, creature, enchantment, instant, kindred, land, planeswalker, and sorcery. Legendary, basic, and snow are supertypes, not card types; Lhurgoyf, Forest, and Siege are subtypes, not card types.

The ability that defines Barrowgoyf's power and toughness works in all zones, not just the battlefield.