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Looking at the line up of champions and considering what each of them is bringing to the fight I do believe Sejuani has the advantage by far.
Ashe leads a peaceful people, or at least more peace oriented then the others, and Aatrox wiped out Tryndies tribe a long time ago so he's not bringing any one else that Ashe isn't already. The other three are basically just coming on their own to the fight, not really bringing any more armies, they just support Ashe's ideology. They can act as generals and commanders though, so that could potentially sway the course of a battle if they're good at it, but only Anivia seems to have the potential for that anyway. She is however allied with Demacia so they could get involved, and they are one of the strongest forces in all of Valoran.
Lissandra has the Watchers so that gives her an advantage, as well as the Troll army lead by Trundle so she has two armies who alone could probably take on that of Ashe's. The downside is it's just Liss and Trundle leading everything, they have no generals or commanders or anything to lead in the field, and if I remember correctly in Trundle's lore he did swear that HE would rule the Freljord once he'd helped Liss beat the other two forces, so there could be some fracturing between those two armies. If another of the armies of Valoran, like Demacia or Noxus got involved it could mean trouble for them as was, since none of the other nations would support Lissandra's army. maybe except Zaun, they like to see new and strange things and tend to get involved in the most random of places just for the sake of experimentation, but they don't really have their own army.
Now looking at Sejuani, her tribe is bred for war, so they could potentially match the forces of Lissandra's and they far surpass that of Ashe's. On top of that Volibear is bringing the whole of the Ursine to join her, which together with the Winter's Claw would easily decimate Ashe's forces and could very likely stand up to Lissandra's and Trundle's. She also has Olaf who will most definitely be leading "troops" into battle, working as a field commander of sorts, which can easily sway the course of a battle against a force who lacks such a role. And ofc Udyr, who also can act as a commander, but is also friends with Lee Sin who is from Ionia so that could potentially pull that whole nation into the conflict. They however have had a kind of stand off-ish history, only fighting when being attacked, so I doubt it. That being said though should Demacia join to help out the extreme underdog that is Ashe's forces then Noxus would most likely join Sejuani. Sejuani and Noxus have similar ideals and Noxus would join any fight against Demacia at this point, and they would not side with the Watchers, cause no one would want to give Lissandra the chance to take over the whole of Valoran.
So yeah I see Sejuani taking the crown lore wise, Ashe's forces being irrelevant and Lissandra's not having the potential for any outside assistance, where as Sejuani has a couple potential reinforcements. The only thing that would change this is if Aatrox got involved, but he hasn't bothered with pretty much any of Valoran's current conflicts and now he's also made himself known, so I don't see him jumping in to sway the tide of battle this time. Not too mention if he did it would most likely be for Ashe, but then Tryndamere would definitely attack him and then Aatrox would have to fight him instead of helping Ashe.