Presumably, the idea is that a planet that is far away, will look somewhat similar to the farthest planet we know, or that blue is evocative of cold temperatures.
In the end, though, I think this is for the same reason why unicorns are pink.
Yeah, so just to be clear; you worded the question as if you think there is such a thing as Planet X. There probably isn't. The "Planet X" you typically hear about is a fiction generated by crackpots, not a scientific prediction (or at best an abandoned one).
Its existence is inferred from the orbits of some Kuiper Belt Objects. Six of them have very eccentric orbits with similar orientations. Astronomers Konstantin Batygin and Mike Brown propose the existence of an additional planet to account for this oddity.
The AASNova page cites this set of representative solution parameters:
planet mass of 10 Earth-masses
semi-major axis of a = 700 AU
eccentricity of e = 0.6
This means going between 280 and 1120 AU with a period of nearly 20,000 years.
That page and the Caltech page also have an artist's conception showing the planet as blue.
This is likely an extrapolation from Neptune, which is very blue because of its atmosphere's methane content.
This planet may likely be kept warm by its internal heat. Uranus (mass 14.536 Earth masses) radiates 1.1 times as much light energy as it gets from the Sun, and Neptune (mass 17.147 Me) 2.61 times (numbers from Wikipedia).
Assuming the same radiation rate per unit volume and scaling to 700 AU, this planet will radiate 1300 (scaled from Uranus) or 1200 (scaled from Neptune) times as much light energy as it receives from the Sun. Thus, a Neptune-like appearance is very plausible.