I really think you're jumping the gun here a bit. The Freljordians as a whole are more or less based off of/similar to Norwegians, Swedes and Finnish people. They share the same characteristics as them: tall, blonde hair, blue eyes (mostly because they are in a cold climate with not much exposure to sunlight, therefore they need to absorb as much of it as possible - basic biology 101 for you right there). And if you look into her backstory a bit more, you will see that they are scattered all over this vast area. Ashe consistently says that they can rise to become a great and powerful nation. Like mentioned above, Noxus is conquering and invading left and right in order to become an empire and it sees the Freljord as an easy target BECAUSE the people are scattered. Imagine having your land, your history, your culture taken away from you and actually put into servitude (which is what NOXUS is doing, not the tribes of the Freljord).
The Freljordians are essentially trying to fight back and keep their lands. They have a natural claim to them, but they do not have the manpower to back it up. Ashe essentially wants to show the South (Noxus, Demacia, etc.) that they exist on the map and are not someone to be taken advantage of. With what she is saying, Ashe is trying to rally her people and bring forth a sense of unity. More things unite them than separate them. And are you sure it's a slave class and not just a lower class? Maybe it's a 'slave class' in accordance with the ancient Roman and Greek term of 'slave': someone who works for a master for a specific amount of time but can earn their freedom. Either way, most who earned their freedom still kept living with their former masters as part of the household. Strength in unity and numbers and there were more hands to help around the house. I'd imagine they would need that in the Freljord to make rugs, coats, prepare the food, keep the house, etc. I don't think their slavery (if it is actually slavery which I doubt) is the same slavery you're thinking of in terms of the American 1700s. There's different types throughout history and they're not all that extreme (HISTORICALLY SPEAKING, I do not endorse any form of slavery, just to be clear).
It seems perfectly logical for the Iceborn to be the main rulers of that area because not only do they have an ancient connection to the land, the weapons and the history, but also to the gods. The Three Sisters (Avarosa, Serylda and Lissandra) are seen as gods and have cult followings (again, like they did in Ancient Greece and Rome - look up hero cults if you don't know what I'm talking about) but we know that they existed because their ancestors Ashe and Sejuani exist and they have a direct lineage to them even though they themselves don't know about it. The weapons they have test their limits, burning their hands with frost and can break people's minds. If we think back to the Vikings and the people that lived in the North, most of their leaders were war-like. It was needed because, just like in the Freljord, they were fighting between them and being invaded (by Rome historically, by Noxus in the game). Someone who cannot wield a weapon like this might not be seen as someone fit to rule.
As was mentioned earlier, yes Ashe does want to exterminate the trolls, but that's more because they are terrorizing the villages and literally eating people. Unlike other monsters that live in those parts (no doubtedly you have read the comics since you are referencing them), the trolls seem to be the only ones capable of having enough intelligence to band together and organize attacks. That being said, they also have enough intelligence to understand: 'Hey, stop eating people!', which it seems, they have chosen to ignore.
Also, the word 'Svaag' isn't used as a derogative term for anyone. In my opinion, it's used more as an invocative term like 'God' (e.g. 'Svaag, I killed you without even trying!' could be seen as, 'God, I killed you without even trying!') I don't think it's derogative like you previously assumed.
Sorry for the long spiel, but Ashe is literally my favorite League of Legends character (followed closely by Xayah) and I don't like people slandering and labeling her as something that she isn't. I also love how Riot put enough thought into the different cultures and modeled them after pre-existing cultures in our world!
