Sejuani wears imposing armor, not because she is weak or can't stand the cold, but because she is a leader and wearing that armor is both very imposing and intimidating, and also appropriate for keeping her alive. The Winter's Claw would fall apart if Sejuani were killed, so it is more than likely that she donned said armor, not necessarily because she prefers it, but for the sake of her people.
Comparing her to Ashe is pointless, Ashe is an archer and would never come into close quarters where armor is necessary. Olaf is probably the most realistically designed of all the freljord champions, since he is wearing a simple leather jerkin and pants, with boots and bracers and his helmet. That matches what most real Vikings wore. You cannot compare her to Trundle since he is an ice troll, not a human, and either way, Trundle wears armor and furs anyway. Tryndamere needs to be updated; his look is from when they basically had zero real lore for any of the locations and having a shirtless barbarian made sense. Now that the barbarians are from the Freljord, I think it would be much more appropriate to make them have more authentic apparel. I have no idea why Riot chose to make Braum shirtless, except for the fact that everyone who wanted a mustachioed strongman wanted him like that. He is really a farmer, and It would be better to have him at least look a little like he ever was one. He does also have a giant unbreakable shield, so he could have decided to forgo armor in favor of just using the shield, so that he didn't have any unnecessary weight to haul around.Nunu, I don't even know if he counts, he needs lore updates and VU to match.Lissandra is from a completely different era, and is also not a front line fighter, so her appearance and lack of armor are appropriate.Udyr is technically a Freljord champion, but he actually is wearing full robes and a giant wolf fur over his head. Spirit Guard Udyr is only bare chested because it represents him after moving to Ionia to meditate.
Basically, each of the other Freljord champion is an individual case and should not be lumped together as a whole. The other humanoid melee champions from the Freljord are all the way they are for a reason, and Sejuani wears armor for her own reasons. Tryndamere becomes unkillable, so he doesn't need the armor (weakest explanation, imo they should VU him with a shirt or armor), Olaf wears light weight armor appropriate to his goal of getting himself killed in battle, Trundle is a troll and wears armor, Braum doesn't need the armor because of his door/shield, and Sejuani wears armor because, according to her lore, her tribe is nothing without her leadership meaning they should take the precaution of guaranteeing that she doesn't die.Their appearances also match their in game play styles. Tryndamere is super squishy when his ult isn't up (fitting since he has not armor), Olaf tries to get himself killed but can't due to his curse, high damage and squishy, but sustains through it like an actual berserker, Trundle is just tanky anyway, and wears appropriate armor for his role, Braum is squishy when his enemies aren't just hitting his shield. Sejuani is tanky, and it is appropriate that she should wear armor, since it reflects to players at a glance what kind of champion she is.
You cannot compare Sejuani to the Amazonian warrior women you seem to think she ought to be, because those are just hyper fantasized champions that are utterly unrealistic. Real Amazons wore the same type of armor as every other warrior in their time period, and weren't imbeciles running around in bikinis, but real hardcore warriors. Additionally, since they were from the then semi tropical area surrounding the Mediterranean Sea, they are not analogous to Sejuani in that way either. The norse women who would be closest to Sejuani in terms of appearance, were almost NEVER warriors, and those that were (there are a few rather notable cases of female raid leaders) usually wore armor virtually identical to the men they lead.