Warning: I am feverish and have induced a headache from a superfluous amount of coughing, so I apologize if this entry is kind of wonky.
When I first was reading The Left Hand of Darkness, I didn't really give the word/concept of "Ekumen" much thought. A little bit later in the book, however, a derivation of the word was given as "Ekumenical." This jumped out at me and reminded me of the word, "ecumenical," for which I (courtsey of OED) will provide a definition: belonging to or representing the whole (Christian) world; general; universal, Catholic; belonging to the whole world; universal, general, world-wide.
Given that Ursula Le Guin is an atheist, I believe that the portrayal and role of the Ekumen as the Catholic Church is one that is subject to criticism or satire. The narrow-mindedness of Catholicism is represented through the narrow-mindedness of the Ekumen's envoy, Genly Ai, who cannot quite grasp the lack of opposites on Winter.
The Ekumen, according to Genly, seeks "the enrichment of harmony and the greater glory of God" (34). I thought it really sounded like the Catholic Church when, on 136, he explains that the Ekumen is not a government, though it may share some similarities to one: "It is an attempt to reunify the mystical with the political, and as such is of course mostly a failure; but its failure has done more good for humanity so far...It is a society and it has, at least potentially, a culture. It is a form of education...it's a sort of a very large school...in another aspect it's a league or union...possessing some degree of centralized conventional organization."
We get the impression that the Ekumen is preoccupied with progress. It is very much concerned with economical profits and gains, and only invites worlds to join if they are sufficiently enlightened or open to enlightenment (both religion-wise and technologically). While some aspects of the Gethenien world are antiquated (Karhide is described as being in a "dark age" ), others are not. Orgoreyn is more industrialized, with standardized clothing. Genly observes that "This, now, looked like a country ready to enter Ekumenical age" (115).
I think it's interesting that in Christianity, it is God who created binaries. He first made Adam, then Eve, a female counterpart. Everything comes in opposites and in pairs. The ambisexual/ambigender? inhabitants of Winter are supposedly the result of some experiment conducted by previous colonists. This dualism and subsequent lack of binaries, though created by humans, seems to be better (in some respects) than the world created by God (no rape, no war, everyone gets pregnancy leave from work....)
Additionally, the random bits of Gethenien folklore or mythology, I felt, read like stories from the Bible. With the story about the Therems and the ending of the book, I got the impression that Estraven was kind of like the prodigal son.
Random thing I thought was interesting: The drink called "lifewater"...I don't know if LeGuin knows this, but "whiskey" (uisge beatha) in Scottish Gaelic translates as "water of life."