How? Easily. The Grimtotem have been dealing exclusively with the forsaken for quite some time to work on a way to wipe out anyone they deem "less than worthy." Obviously, with the events of the Wrathgate, the forsaken have failed in a very major way and are currently under the watchful scrutiny of the rest of the Horde until they prove that the events of the Wrathgate aren't going to occur again. Upon realizing this, Magatha decides that the best course of action in order to continue what she's quietly trying to do (wipe out all inferior races on Azeroth, aka anything that isn't a Grimtotem) would be to take the place that the forsaken previously occupied, that of an advisor and ally to the Horde itself, speaking on behalf of the tauren people.
Given Magatha's outlook on the Alliance, her people's actions toward the Alliance in Dustwallow Marsh, and her people's predisposition to violent behavior, she would get along quite nicely with Garrosh, who is far too young and naïve in the ways of Azerothian behavior and politics to realize he's being played. As for where this leaves Baine Bloodhoof, Cairne's son -- it leaves him to quietly lead a small faction of tauren who are very, very unhappy with Garrosh's actions.
Which brings us to the second possibility: Garrosh frames someone else for the deed, say ... the Alliance, as they're an easy target and Garrosh would very much like them out of the picture to begin with. While the tauren aren't the war-seeking sort, I'd say the death of their beloved leader at the hands of "the Alliance" would be more than enough reason to want the Alliance eliminated. Especially if the one left behind to lead is the grief-stricken son of the murdered, beloved leader, who now has Magatha simultaneously comforting and egging him on. Wait -- grief-stricken leader, evil presence up to no good quietly guiding things while he's wallowing in despair ... This situation is beginning to sound awfully familiar, isn't it?
Another solution that hasn't been considered or addressed is that the tauren of Thunder Bluff and the surrounding areas have been kicked out. The "tauren" currently living in Orgrimmar are going to be Taunka, not the tauren we're familiar with. These taunka haven't really seen anything of the Horde but the face they showed in Northrend -- the face that was led by Garrosh Hellscream. This is a long shot though, and doesn't have a lot to back it up beyond, "Well, the taunka seemed to be okay with Garrosh up in Northrend, and they're not really the sort to object to violence."
And one more solution that nobody's even bothered to contemplate: Garrosh didn't kill Cairne. Cairne simply died naturally of old age. He was terribly old during Warcraft III. He's lived a long, full and happy life, and one night he simply went to sleep, dreamed wonderful dreams and didn't wake up. Baine takes over tauren leadership in his father's stead -- which still leaves the "Magatha is going to simultaneously comfort and manipulate the poor grieving kid" theory entirely open.
Political struggles, huh? You mean like the jerk who has little to no resemblance to that shaman you swore your allegiance to, the shaman that tried his absolute hardest to save your father, the beloved leader of your tribe who is suddenly being placed in charge? The one who obviously views your people as weaker citizens, given that you weren't even asked or stationed in Orgrimmar, that you and your tribe weren't viewed as strong enough to handle attackers? Your tribe, descendants of what was once one of the mightiest empires Azeroth had ever seen?
Or maybe it's that you know something, Vol'jin. Maybe it's that you saw or heard something you shouldn't, but you haven't got any real proof. Like that jerk we just talked about, maybe you happened to catch something about him that was so horrible, so reprehensible that you're not sure anyone would even believe you unless they were given solid, irrevocable proof. ... Something like the cold-blooded murder of one of the most noble, beloved leaders of the allied races of the Horde.
Yeah, that'd be what I'd call "political struggles" too, buddy.
Obviously from a writing and design standpoint, the blood elves are not going to fracture from the Horde altogether. Like the forsaken, however, they've reached a point where they simply have nothing to do. While I have no current theories on what role the blood elves are going to play in the new Horde that Garrosh is throwing together, it would be safe to assume that they'd be just as annoyed about being considered weak as the trolls and forsaken are. Given that the blood elves are being granted the warrior class, it could be possible that those warriors are being trained specifically to show Garrosh exactly how strong elven society can be.
And the elves don't seem to hate the Alliance as strongly as they had in the past. The redemption of the Sunwell was at the hands of an Alliance member, regardless of who they were working for at the time. And the blood elves are giving the Silver Covenant, an Alliance organization, access to that Sunwell (albeit cautiously). There's not really any other information out there about the blood elves and their role in Cataclysm; however, recent events suggest that keeping an eye on the blood elves and their activities would probably reveal some interesting new beliefs or new plans.
The kink in the rumor involving Thrall's ascendance as Guardian is this -- there's already a Guardian. His name is Me'dan, and you may be familiar with his parents, a half-orc named Garona, and a former Guardian by the name of Medivh, the supposed "last" Guardian of Azeroth. Me'dan is quarter orc, quarter draenei and half human, an odd combination to say the very least. In the Warcraft comic series, he was appointed Guardian by Jaina Proudmoore, who had some incredibly curious things to say about the whole Council of Tirisfal/Guardian situation.
What sort of things, exactly? That the actions of Malygos affected the mages of Azeroth, that their powers had weakened, and none of them were strong enough to form a complete Council of Tirisfal or take on the mantle of Guardian. So Jaina asked practitioners of different kinds of magic -- shaman, druid, priest, paladin and mage -- to combine their efforts and diverse magics into a new form of the Council of Tirisfal and appoint a new Guardian to fight as champion of Azeroth.
Since the Lich King has been defeated, Thrall and his people are no longer at war. Azeroth has been torn asunder due to Deathwing, and his emergence ripped open holes into the Elemental Plane. Elements and the earth are specialties of the shaman, and Thrall is supposedly one of the most powerful shamans alive. Given that according to the comics, a Guardian is essentially a person who is imbued with the powers of several other magic users all at once, it's entirely possible that the Council could decide that a shaman Guardian would be best suited to fight the elements and the former Earth Warder.
... Or Me'dan somehow met an unfortunate and messy end, and we simply haven't seen how yet. Or Me'dan decided he was tired of being the Guardian and would rather continue to study and hone his control over the power of the Light. Or Me'dan and the events of the comics simply didn't exist in the current universe, a retcon of the tales that were told in the comics. We don't know exactly, but it's not impossible for Thrall to take up the Guardian mantle, because all the writers have to do is find a logical way to fit it into the existing story, something that is entirely possible as illustrated above.
Or Thrall, in a fit of uncharacteristic annoyance, decided to give the orcs of the Horde who supported Garrosh exactly what they wanted -- so that those orcs would see that what they wanted wasn't what they thought they wanted and wasn't what they needed in the long run. In any case, it is unlikely that Thrall would leave for long -- or that he would stand back and allow the orcs, his people, to callously slaughter the Alliance with whom he'd tried so hard to forge some sort of semblance of peace.
Yes, this is another prediction. I think that somewhere in Cataclysm, Garrosh will either discover the error of his ways in spectacular fashion ... or Thrall will come back and show him the error of his ways, using his fists. And lightning. And the elements. And anything else that happens to be handy, and it will be epic.
I feel like I'm forgetting something ...