The Horde has never been exclusively tribal/nature themed. Orgrim Doomhammer set entire forests ablaze, they've used Demolishers since WC3 and allied themselves with Goblins twice. To paraphrase Blizzard the Horde is "a group of outcasts that banded together as a dysfunctional family and work to reconcile their differences and win the day". In other words, the Horde is a patchwork of different ideals and cultures that united under a common cause(rather than the rigid ideals and common culture of the Alliance), that "natural loving noble savage" you are alluding to is just another square in that quilt.