I wouldn't exactly call the Horde an anti-hero faction.
Lets review all Horde races.
Orcs.
Before the coming of the legion to their native world, they were a shamanistic race, communing with the elements and keeping the balance of their world in place. Then, the Draenei arrived which attracted the Legion and the result was Orc corruption. Now, on Azeroth, the orcs have more or less regained their shamanistic ways, but acquired a bloodlust that has been injected into their roots when they drank the blood of the demon pit lord. Needless to say, the Orcs, alongside all other races of the Horde and Alliance are concentrating their lust for battle on a common enemy (The Legion, The Scourge) while they could very well be waging all out war on the Alliance like they did during the great wars long ago. From this point of view, I believe that the Orcs, and especially such personas like Thral and Saurfang, are a very heroic race, a fact that people tend to ignore due to their violent nature.
The Forsaken.
At first (during the WoW classic days), I would probably also be chanting that the Undead only use the Horde for their own needs (destroying the Scourge and the living that hunt them down), but ever since some of the new expansions they seem to be more and more loyal and patriotic towards the Horde. Perhaps that is because of the Blood Elves joining them. The Wrathgate incident was organised by rebel alchemists and Varymanthras and Sylvanas herself was cleaning that mess up, so this can't be considered a negative act from the Forsaken, since not all or even the majority of them were involved or were even informed of this. The Forsaken have made the Horde their rightful place and help them fight for a common goal. I don't believe that after having her revenge on Arthas Sylvanas would just withdraw herself and her followers from the Horde to live in solitude.
Tauren.
There's not really much to say about the Tauren. They are probably one of the most noble races on Azeroth. Being shamanistic and always heeding the call of the Earth, their prime goal is to keep the delicate balance of nature on Azeroth. Also, can anyone recall any marauding or slaughter done by the Tauren (besides Grimtotem tribe, which aren't part of the Horde)? No? Didn't think so, moving on.
Trolls.
Same story as with the Tauren. They have many tribes in the world, yet all share a similar bond with nature. The Darkspears are the only tribe that is in the Horde and are also not known for any evil deeds, like the Gurubashi or the Amani. In fact, Darkspears are one of the forces that fight against the ''evil'' trolls.
Blood Elves.
Ok I'm not going to state my opinion much here, since I really, really, really dislike all kinds of elves. I'll keep it short: Kael'thas and his possy in Outland are the ones responsible for summoning Kil'jaeden through the Sunwell, the elves back on Azeroth had no idea and after finding out, joined the other races to defeat him.
Right...I think I covered the most important parts here. If anyone remembers something else, let me know.