Adding to what others have said:
The semiconductor part of a modern white LED is well-known. There are thoroughly tested models for how semiconductors age, and as long as they're kept cool (<50°C), and not driven too hard, they last almost indefinitely.
However, most white LEDs are in fact blue LEDs with a phosphor that converts some of the light into longer wavelengths, and this phosphor can also age. This is also aggravated by excessive temperature, but I believe that the effect is less pronounced - which means that at low temperatures the phosphor ages faster than the LED per se.
When the LED ages the light intensity decreases (the stated lifetime is the time until the intensity is halved.)
When the phosphor degrades, however, the light changes colour, probably towards the bluer end of the spectrum.
Still, neither of these effects should be of any concern for a Paperwhite user, unless you're using the device for more than ten hours a day, in a sauna.