Can Jupiter's nightside be classified as spectral type Y?
This Wikipedia page lists Jupiter as a disputed sub-brown dwarf because its mass reportedly is sufficient to qualify for one. Distance to another star like the Sun doesn't matter, nor does the visibility in the infrared spectrum either since every planet is emitting some infrared light. The fact that Jupiter emanates more energy than it gets from the Sun can't be accounted for either, since that's also a matter of distance from the Sun, and Saturn and Neptune do so too. But, as the article states, Jupiter obviously has enough mass to possibly count as a sub-brown dwarf. Sub-brown dwarfs are still planets because they don't undergo nuclear fusion unlike brown dwarfs and hydrogen-fusing stars and never did.
Edit: There is no reason to only classify the night side just because the day side is illuminated by a(nother) star. Spectral classifications are given to the entire object. Since sub-brown dwarfs reportedly have a mass of at least one Jupiter mass, you may want to classify Jupiter a Y9V sub-brown dwarf.