Such an excellent book! And yeah, every single Estraven chapter ended too soon.
If you haven’t read the short story or two also set on Gethen (Winter’s King, and Coming of Age in Karhide), they are worth a read. (As, of course, is pretty much everything Ursula Le Guin ever wrote, because, damn.) Both do address the original sin of using the male pronoun as the default in the English version of the Left Hand of Darkness (which has me wondering about translations of her Gethen stories, but more on that in a second) - it’s somewhat fascinating to see how much that subtle little switch matters, with the most visible change (for me) being in how I imagine the kings of Karhide. The first story is more in Le Guin’s mythic/fairy tale mode, and the latter a smaller and more purely personal/anthropological exercise, but both are actually from Gethenian points of view, rather than Earth/Hainish ones.
A possibly interesting contrast/corollary on the role of gender is another short story of hers, The Matter of Seggri. (The conceit in brief: male babies are significantly less viable, the social role of men is more or less constrained to breeding and entertainment, attempts to deal with this after the arrival of the Hainish are… complicated.) Contrasting the depiction of the primarily female society on Seggri with the genderless society on Gethen made it clearer for me, I think, the difference between single-gender spaces (as Le Guin sees them, at least) vs. truly genderless spaces. Which is somewhat subtle, and which is complicated by the way Genly’s POV in Left Hand of Darkness feminizes bits of Gethenian culture that he doesn’t understand. But as someone who’s generally bemused and discomfited by gender, I definitely agree that what I valued was less Genly’s thoughts on gender, and more what you describe as leaning over Estraven’s shoulder, watching Genly with an arched eyebrow. (Although I don’t know that I’d describe Estraven as female; Not Male sounds closer to right, to me, and honestly Not Female as well, and it’s an interesting exercise considering what it would have been like, were Genly’s place taken by a female Mobile.) And as the story goes on, Genly does spend a little less time trying to force his interactions with Gethenians to fit into the gender binary (though he never can quite stop), until we reach the end where upon seeing his shipmates again, he thinks “But they all looked strange to me, men and women, well as I knew them […] They were like a troupe of great strange animals, of two different species.” (Arguably, my “[THAT’S] HOW I FEEL INSIDE RICK. ALL THE TIME.” reaction to that passage should have clued me into the fact that I wasn’t super down with the gender binary myself, but hey, I can be a bit dense.)
Along somewhat similar lines, if you haven’t read Ancillary Justice, you might find it interesting; while rather more of a Space Opera ™ than anything Le Guin ever wrote, and without Le Guin’s particular compassionate yet anthropological touch, it’s also, among other things, an interesting look into a very different societal approach to gender than ours, albeit without the biological underpinnings seen in Le Guin’s Hainish books. “An ice planet plays a major role in the first book too.” Anyway, the society at the center of most of the book (and its two sequels) is genderless, despite having biologically distinct sexes; major social divisions come much more from class, clan, and patronage. I was reminded of it because while I don’t recall having seen any articles about approaches to translating Left Hand of Darkness, I did read one regarding translating Ancillary Justice (no spoilers) and the challenges that the use of feminine pronouns as default imposed on translators in a range of languages.