Oh, this is fun.
Keep in mind everything's speculation at this point. If you have a completely different read on the situation, that's cool.
First, and I guess quite logically, the fact that Yuki-onna are kind of in charge means that women and not men are seen as sexually aggressive. I'm going to guess that a lot of myths are re-interpreted from the yuki-onna point of view and told as morality tales about the pitilessness and hunger of winter, and hey, men who wander all alone on a lonely winter path are going to get gobbled up by the first yuki-onna who you cross paths with, tsk, tsk, ask not why the scorpion stings the frog, nor why the Yuki-Onna desires warmth, it is in their nature.
Tl;dr: Gonna guess that their little red riding hood is a man and that any Orpheus and Eurydice exchange places.
Men in this society seem to be the care-givers and nurturers. The fact that Ostrik has candy ready for small children and seems to be treating Ling Qi as a single father does make me review past assumptions about the relationship between the nomadic tribes and the ice people in a new light: before, my working hypothesis was they needed more manpower for something akin to slave labor, now it's a lot more up in the air. Are they giving them as tribute to Yuki-onnas? Do they need more men because men can attract solar unicorns and keep the Outer Night at bay? Lots of speculation, not enough lore. Need more information, basically.
The arc, then, of the male deities seems to be: Koliada, the joy-bringer, inspirational, beautiful - maybe a bit like Balder of Norse myth whom everything cried for after he passed away, but less emphasis on the beauty, and more emphasis on the joy-bringing and inspiration. Basically, your jovial uncle, your fun older brother, your dad jokes and etc. Gan Guangli hilariously falls right into that mold so knowledge of him being unattached is probably going to end up in hijinks. Perkunas, the Stormbringer, who gets the least description, but can probably be assumed to be a lot like Thor, kind of stupid, impetuous and prone to solving problems with his fists or hammer. Perkunas seems to be associated with Outer Night, which suggests to me that his role in the pantheon was usurped given that he's nominally a solar deity. Add to that the fact that he seems to be a devil-like figure and you get the impression he was a war god, but the culture shifted due to X event and now he's become an 'enemy', and the fact he's still honored as part of a trinity is a holdover from a past age.
(It does bring up an interesting parallel with the Empire though, while I'm out here speculating: an aspect of the sun sacrificed itself, and here we are with what looks like a broken trinity - I doubt they're related though, we'd have to start doing comparative history/mythology in order to check that out. Seems like a fun project for a visiting scholar even if the end result is: nope, they have nothing to do with each other)
Finally, the Crowfather, the wanderer, wise and mysterious. An Odin-analogue. He's probably got a lot of fun stories, but at this point, you can just think of him as a wise man that wanders about, that's all we know so far.
This is extra fun for me because the next trinity begins with a Wanderer - the Emissary. It gives you the impression that either the arc of male development and female development are either inverted or in sequence - men slowly become more like women and women slowly become more like men; or that men only ever reach the beginning of the female role at the end of their lives. I'm probably wrong here though, it seems more likely that these two pantheons fused, much like how it's hypothesized that the Aesir and Vanir (again, Norse mythology) used to belong to two different pantheons before one conquered the other and absorbed their pantheon.
The female spirits/deities are interesting because they always seem to have a dual nature except for the youth: the scepter/crown/orb are traditional symbols of rulership, the axes and the nakedness (sex and violence), the mortar and pestle and the chain of skulls (death and life). The Youth seems to most closely identify with the Yuki-Onna - the virgin iconography replaced instead with Rulership, perhaps also hinting at the fact that the Yuki-Onna do not reproduce. And since Yuki-Onna cannot be mothers (it is not in their nature to reproduce), the mothering role then falls upon the opposite gender - men, who are warm and giving in a way that women cannot be. The Youth is a closed circle, perfect and sterile, someone who can wander to and fro and not be affected. This is probably important to them, given that whatever the Outer Night is seems to capable of psychic contagion. If you look at the crown, it is a symbol of holiness, an emulation of an angelic halo (and, one assumes, here a symbol that one can protect oneself from the Outer Night); the orb a symbol of power, traditionally from the earth and land, here from ice; and finally, the scepter, from direct contact we know that it can serve both as a weapon and as a means of protection, probably a symbol of self-support and defense of the dominion that they rule over. The dual nature, I'm going to guess, is in its very existence: the Youth represents a bridge between mortal and divine, human and spirit, the joining of which is invested with authority.
The mature woman is usually where the mother would be - care-giver and nurturer, except her aspects have been inverted. She is aggressive and wild. This is a clear counterpart of Perkunas, just gender-flipped. Now, if she too has been subverted like Perkunas has been and is considered something of an 'evil' goddess, I can assume that the trinities are balanced and that maybe they evolved naturally to have two positive aspects, and one negative aspect. If she hasn't, and is considered a war goddess that is honored as such, I'll assume that she's usurped Perkunas' more positive aspects due to whatever it was that made Perkunas lose his place. She probably represents desire: lust, battlelust, hunger and all the rest. She consumes others and in that consumption, finds a way to continue existing.
Finally, the crone. Life and Death are kind of a big deal, and the crone embodies both. Just like Meizhen told us so very long ago, as elements they tend to affect cultivators more easily and more permanently. That you have both in one deity says a lot. If I were going to guess at her role, I'd say she'd be an arbiter. A judge that stands between crossroads, one who chooses between life and death. And the wise woman is essentially that: a healer, but also someone who decides what must happen.
I think, coincidentally, we map out fairly well to all five aspects. Well, then again, that might just be a generic personality test at work and us all having very different personality types.
Nevertheless:
Ling Qi is the Emissary, invested with the authority of blood and spirit. Her husband is Gan Guangli, the joy-bringer.
Xia Lin is the champion, the warrior woman. She does not have a husband.
Cai Renxiang is who they called Oathholder, the power behind the power, one who has the power to make the decisions that seperate life and death. Her husband would be Meng Dan, the wise old crow.
A lot going on below the surface here, I'm truly quite impressed with the worldbuilding, it goes down smooth af. Hats off, Yrsillar.