Oooooooooookay. Well, this is a tough one and off the top of my head I don't know who would win, so lets break everything down and see where that leaves us.
(Going to apologize in advance, my lore knowledge isn't super up to date on either group so mb if I make mistakes)
Lets cover the armies first this time. Both sides have large numbers of quite powerful warriors, that being said I would say that Freljord has the upper hand in individual skill/small group tactics. On the larger scale of things Noxus definitely has the upper hand, a larger troop reserve (The Freljord simply can't support the population density of Noxus) as well as some neat tricks, such as the minotaur tribes. Freljord does have the trolls,Yetis, and Ursine though, which I would rate to be as scary as anything Noxus could pull up. Again, my specific knowledge is lacking, so feel free to mention if I missed any monsterous creatures on either side.
All in all I don't think it would be clean or easy, but I believe that when it comes to armies Noxus has the advantage. They are a nation built on and for battles like this after all.
Spellcasters are also an interesting thing to note here. Noxus has quite a number of them and I believe they are treated well in the Freljord as well, though aren't as numerous or as combat focused. As such Freljord would not be at the spellcaster's mercy, but I do think they are at a severe disadvantage, especially since I doubt Freljord supports any formal training for their mages due to how fractured the clans are. They are most likely taught by older clan mages, whereas Noxus would work to train and weaponize their magic users.
Now on to the juicy part, the heroes. Lets start with Freljord.
First of all Tryndamere and Olaf. Interesting the lore for these two is basically the opposite of their in game lore. Tryndamere is not actually undying, simply able to keep fighting further than normal. In other words if he loses his head he is dead, enough said. Olaf on the other hand is interesting. Since he can't die in combat he would definitely be trouble to deal with. Interestingly so long as he wasn't executed via Draven then he can still be captured and killed later. Thus he is definitely a big threat, but not unstoppable by any means. In fact if he tried to actually kill all of Noxus by himself he would probably die from the forced strain of constantly traveling from one section of the army to the next, not actually in combat. Again though, his is a simple case of restraining and killing later, and he doesn't have any ability to break free of magical restraints or sufficient physical ones.
Next lets cover Lissandra. Definitely scary, and a mage powerful enough to contend with Swain and Leblanc. Interestingly I would actually rate her slightly above Leblanc, as they are quite similar in their ability to copy identities though Lissandra has more combat power due to her ability to warp True Ice. Her deception does not quite match up to Leblanc's range though. Personally I do think she could be defeated, perhaps even by enough of Noxus' normal mages. She was created by the watchers after all and would thus be weaker than them (as well as only being one person) and the Watchers were defeated by a single group of heroes. (Update from Trundle's lore, apparently she has Guardians, but a lone and not very powerful troll was able to defeat them. Trundle was also able to outsmart her traps and she had to face him herself. This implies she is not actually very powerful when not present, which isn't a good sign of her ability to deal with armies as range trumps all in these types of battles (so long as you have sufficient firepower))
Trundle: Not overly strong, but with "cold power running through him" from his club is a fairly powerful troll. Most of his ability actually lies in his cleverness though. As such I wouldn't actually rate him much higher than the rest of his trolls (see army section). Freljord has numerous tacticians, which is actually fairly nice, but when it comes to large scale war I doubt they match up to Swain and definitely don't have his global presence and ability to command multiple places at once. Their numerous tacticians do allow them to have a similar coverage of on the spot tacticians though, so while not as cohesive as Noxus they do still have good leaders.
On to the big hitters: Ornn, Anivia, and Volibear. Currently Freljord is down without even covering all of Noxus so these three have to win the rest of the war themselves.
"The resultant cataclysm was a storm of fire and ash and lightning so intensely violent that it was seen ten horizons away." Okay well that is just 2 of them fighting so we know we are in for some power. Or is it? If we are talking about flat ground 10 horizons away is a 30 mile radius, which isn't bad but that means that two of them aren't even matching Xerath. However this was happening on top of a mountain, so that range expands significantly. Assuming a 20,000 ft tall mountain (Pretty reasonable IMO for a God's home.) That leaves us with a battle that is visible over 1,500 miles away. Now we are talking. It was also enough to completely destroy a town at the base of said mountain, which we will just say is 20,000 ft away since it is a slope but probably doesn't go down to sea level.
Anyways, 2 of these Gods clashing at what we assume is at or close to full force creates, at a minimum, a 20,000 radius of destruction, even to incinerate bodies but not the bones. Interestingly enough that is roughly twice the size of an Atomic bomb kill zone, and since the fight ended after that we can assume each of these three are capable of exerting the power of a bit more than an Atomic bomb before needing to rest/recover, minus radiation zone.
Want to briefly touch upon Anivia, as hers is an interesting power. She controls all the weather in the Freljord, meaning that Noxus would be at a MASSIVE disadvantage fighting there. However she is also bound there, and isn't capable of utilizing such power outside of said area. Since no location was ever laid out for these battles I will assume a neutral territory bereft of unusual advantages for either side. I will consider Anivia to be allowed to participate, but I do not consider her complete control over weather to apply, and will power gauge her based on Ornn/Volibear.
Last interesting note before we move on to Noxus, it is specifically stated, for all 3 of their bios, that they are Demigods, emphasis on Demi. We also know that all such beings (Even Asol) are able to be killed, and thus I do not consider them immortal, simply... difficult. Definitely more powerful than an ascended though, and other than Ornn they are decently ranged. (Volibear literally throws lightning bolts from the tops of mountains.)
Alright, well you won with the armies, but as dumb as they are 
Noxus forces don't currently beat armoured lightning bears. So lets see what else you've got.
Swain and Leblanc. Gonna group these two together because I feel they fullfill a similar role at a similar power level. I don't think they can compete with the gods of the north but I do believe that through their massive range, deception, and incredible intelligence gives Noxus as a whole an incredible boost. Even with incredibly powerful beings, wars aren't won by the work of a single person, and while their raw power may rate them at a 2, their abilities are so well suited for wars such as this that as assets I would place them in the high end of 3 at a bare minimum. In a time where long distance communication is difficult, the power to command and deceive from afar is absolutely bonkers. Also worth noting that Lissandra was able to kill and important members of society and pretend to be them for long periods of time without being noticed, and Leblanc is even more skilled in that area without needing to be quite as directly present as Lissandra. Honestly with Leblanc in the mix I heavily shift the armies in Noxus' favour significantly (Formerly painful fight with a Noxus victory now a far easier fight for Noxus)
Vladimir. Well hello to you too. What's this? Another Noxian capable of mentally messing with his foes, and not only that, but able to completely turn off Olaf? How interesting. What's this? Trolls, Yeti, and Ursine oh my! Welp. With those on Noxus' side there goes any hope of Freljord's army winning. I don't think he could stand up to the gods of the north due to them probably not having proper blood (and even if they did...) Same goes for Lissandra, her veins flow cold now. Interesting I think Tryndamere might actually be able to resist. In his lore he withstood death based on Willpower alone to stand up to Aatrox. Braum may have hope for a similar reason. Unfortunately half the people able to resist him are probably dead just from the standard armies and he shuts down one of the few problematic members (Olaf) CC immune only in game, what a shame. Unfortunately we just don't know enough about his offensive power, he will certainly have plenty of blood to work with though.
Kled. C'mon, just because I tend to skip weaklings doesn't mean I can just pass over our first Yordle. Which is actually an interesting point, what lore are we considering confirmed? Only lore from stories/bios? In that case he isn't gonna help much, however if we are taking Rioter comments on official lore then Yordles are basically spirits. Frankly we don't actually know if and how they die, they live for a long ass time though and most people don't see them as what they are, in fact off the top of my head no one is actually confirmed to. Even Demi-gods may not be immune. Not very useful in combat but an interesting thought. Anyways if it weren't for the fact that he is a complete coward Kled does have Skarl, which isn't actually something even the gods of the north can kill. I mean Skarl can't do much either but let be honest, counting on Skarl is just a bad idea in the first place.
End of Part 1, RIP text limit.
and 
will be working together. With coven after coven of coven of spell slingers and the powers of enslaved demons, Noxus could evenly place soldiers throughout the Freljord and still have them able to make out the color of their hair under their helmets.
is better.
taking control of the warbeasts of the Frejlordians and their commanders.
, but they would eventually fall with hundreds of mages constantly shooting at them (maybe "hundreds" is a little too much to say but my point still stands)
or 
would have a clean fight against the likes of 
or 
. And then 
sounds scary upfront, but he might meet his match against 
... Either way it doesn't matter because the deal breakers are the demi gods.
(who isn't all that hard to kill considering the other champions on this list.) He can learn about 
.
Darius conquer.