Southron Invaders and Foul Horde

[Sam, Great Elf Warrior]

Exactly. Simply searching for Ambush does not activate all abilities that mention Ambush.

As for Ordnance Grunt and Gollum, Plotting Deceiver, their abilities specifically make themselves active while in the discard pile. Nothing in Foul Horde's ability makes itself active while in the discard pile, nor does Southron Invaders's ability activate texts that grant minions ambush. Otherwise if there was a condition that said, e.g., "While you have initiative, all minions are ambush ," Southron Invaders could let you play anyone as long as you had initiative and that condition was in the discard pile. Southron Invaders only activates the ambush keyword of minions in the discard pile, because that's all it's looking for; abilities that merely mention ambush are unaffected.

Additionally, game texts only affect cards in play unless they specifically affect out-of-play cards. While Foul Horde is not in play, no game text, including its own, can affect it (except texts that specifically affect cards not in play, e.g., Southron Invaders or Ordnance Grunt).