First general information: Gethenians are androgynous for about 3 weeks every month (period called "somer"), then they develop gender (male or female - any Gethenian can both sire or bear children) based on pheromones produced by nearby people - exposed to male pheromones Getenian would turn female and vice versa. This time of the month is called "kemmer" and it is treated as special, bonding time within community, although people who purposefully extend their sexual period are treated as perverts (hence in the books humans are often viewed as such).
Now when it comes to the gender pronouns - from the afterword to The Left Hand of Darkness Le Guin addressed this issue:
Having invented a race of people who are essentially sexless except for a few days a month, when they become very highly sexed either as male or female, and for the duration of pregnancy and lactation, when of course they remain female having discovered the Gethenians, what was I to call them? In 1967, when I wrote the book, I called them all "he." I believed then that the masculine pronoun in English was genuinely generic, including both male and female referents. This is a pleasant and convenient belief. Unfortunately, the more you look at it, the less credible it becomes. Even more unfortunately, it has been adopted as one of the Thirty Nine Articles of Antifeminism. Some years after the book was published, I lapsed from the faith, and have remained unregenerate ever since. "He" means what it says, no more, no less alas!
Therefore the author decided to change it:
It has often been suggested to me that the way to avoid the false generic "he" is to use "she," at least part of the time. Dr. Spock calls his Generic Baby he in one chapter and she in the next; this is a nice solution to his problem, but it won't do for my Gethenians. It would merely seem as if they were always alternating male and female kemmer, and never were in somer.
Le Guin experimented with her own pronouns:
I use a for a genderless equivalent of he or she; en for her or him; es for her, his, hers; and enself for herself, himself. The pronoun "e" will probably look to many readers as if it should be pronounced like the letter, rhyming with "see." I pronounce it with the short "e" sound as in "yet" or "them."
But she wasn't entirely happy with that, because it was starting to look too strange. So in the end:
In the reprinting (and all subsequent reprintings) of the Gethenian based story "Winter's King," I kept malegendered nouns such as king, lord, but changed all the pronouns for Gethenians in somer to the feminine. The effect is very interesting, and was effective, I think, at short story length.
But that wasn't the end of it:
In the second of the following texts, I have done the same thing to the first chapter of Left Hand, changing all pronouns for Gethenians in somer to the feminine. But this time I also feminized the personal nouns king becomes queen, lord becomes lady.[...] But when all is made feminine, it is as untrue to Gethenian reality as when all is made masculine.
Pursuing these experiments, I have repronoun'd a couple of passages where people in somer go into kemmer and come out again. In the tale "Estraven the Traitor," I use my invented somer pronouns, switching to English gendered pronouns at the appropriate moment. I rather like the shock effect. In a passage from chapter 18, I keep to the usage of the original text, calling Estraven he, until "he" goes into kemmer and becomes definitively, in anybody's language, she.