So the contrast here is between timeless, (relatively) unchanging beauty, like the sterile, pristine, immaculate beauty of the stars in the nighttime sky -and fleeting beauty, like the desert in full bloom, or the pattern of ice crystals on a window, or the starburst explosions of fireworks. Part of the experience of enjoying fleeting beauty is the lust to drink it all down while you can, to burn it into memory for future reminiscences.
Shimamura spends a few weeks each year in a resort tucked up in the mountains of the titular "Snow Country" of Western Japan. The rugged terrain and natural rock formations are timelessly beautiful, but he meets and falls for Komako- a geisha whose allures are decidedly fleeting. Geishas in general have their youth and charm squeezed out of them in a very short career, and are then discarded. Supposedly- as the narrator explains- this is never more the case as in resort towns up in "Snow Country". The constant supply of monied guests attracts a lot maiko (young geishas) to the area. It seems there is always a younger, fresher face showing up on the scene.
Fleeting too, is the romance between these two characters. Just a few days after meeting, Shimamura will have to return to his life in the city.
The short affair makes its impression, and Shimamura finds himself returning in subsequent years. On one hand, there's an element of "you can never go back", because Komako's looks are on the decline, and familiarity dulls her charms, but Shimamura (and the reader) discovers details about her in layers, which flesh her into more of a three-dimensional person, rather than an object of nostalgic reverie, or an expired ideal of beauty. Through this discovery, we see a hint of the timeless beauty of her inner life, her thoughts and history- things she's never shared with other customers as a geisha.
Focusing on this alone would have made this a beautiful 5 star book, but I have to say that the execution is a little botched by a Shimamura's constant navel-gazing, and a storyline about Komako's younger, more beautiful housemate Yoko, which is distracting and goes nowhere.
The author won the Nobel Prize for literature in 1968, and then committed suicide in 1972... two facts which I'm sure are not even slightly related, but nevertheless seem to make a powerful and sincere statement about the fleeting beauty of a Nobel Prize in literature.