Why do some Asian dragons have fur (or hair)?
In the west, we tend to think outside dragons as purely reptilian in nature - in other words, all scales, no fur - but many Asian representations of dragons show them with substantial amounts of fur (or hair).
This is even true in more recent depictions of dragons from the east - these two images were produced by the Japanese animation company Studio Ghibli:
Why is this the case with Asian dragons, and why the discrepancy between Asian and Western dragons?
By fur, do you refer to the hair on their heads? Canonically, Chinese dragons (from which Vietnamese/Japanese ones derive) have fish scales on their body, and your examples match this.
@Semaphore - See my two most recent additions. In any case, they are all 100% furrier than western dragons, which have no fur at all.
It's possible that the Chinese based theirs off a creature that did have a mane-like feature. Despite their common depiction, many dinosaurs had feathers.
It is important to note that East Asian dragons are in fact quite unrelated to Western dragons. While they may have influenced each other, the two traditions emerged separately. They share the same name essentially only because of translation choices; there is fundamentally no reason why Chinese dragons shouldn't be different to European ones. Hence, the hair disparity ought to be unsurprising since they are not the same creature in the first place.
Secondly, East Asian dragons do not have furs in the usual sense of the word, although they are often depicted with beards or manes. Canonically, the body of the Chinese dragon (from which Japanese, Korean and Vietnamese dragons originate) have fish like scales. While the exact appearance have varied over time, the fish scaled body has remained a constant feature of dragons in the Far Eastern tradition.
As early as the Han Dynasty, a scholar named Wang Fu introduced the concept that dragons resemble nine animals. The Ming Dynasty and scholar doctor Li Shih-chen writes in his magnum opus the Compendium of Materia Medica that:
龍者，鱗蟲之長也，王符言其形有九似：眼似兔，角似鹿，嘴似牛，頭似駝，身似蛇，腹似蜃，鱗似魚，爪似鷹，掌似虎 ... 口旁有鬚冉，頜下有明珠。
Dragons are the first of the scaled beasts. Wang Fu says it resembles nine animals: eyes like rabbits, antlers like deers, mouth like cows, head like camels, body like snakes, belly like shellfish, scales like fish, claws like eagles, and paws like tigers ... its mouth is bearded, and there's a bright pearl below is jaw.
More relevant to visual depictions, a traditional mantra for dragon painting is:
First, deer antlers. Second, shrimp eyes. Third, dog nose. Fourth, cow mouth. Fifth, lion's mane. Sixth, fish scales. Seventh, snake's body. Eighth, fire flames. Ninth, chicken's breast.
These traditional descriptions of dragons also gives us some insight into why the Chinese version has hair. Whereas the European dragon has a strong reptilian quality, their Asian counterparts are considered a composite of different beasts - many of whom has plenty of hair. Thus, despite a (probably) serpentine origin, the Chinese dragons acquired hair on the head and limbs. These were also the same body parts that did not come from fish or snakes.
Note that the protrusions on the back of the dragons are not hair, but rather backfins. This is an ancient feature of Chinese dragons, dating back over three thousand years to Shang Dynasty era depictions.
See below for a Song Dynasty conception of the dragon, painted by the artist Chen Rong. This was about 1000 years ago,
IMHO The question's anime dragon and 3D art examples do not really depict traditional dragons.