the.com/cold comfort

means Something meant to console that barely helps at all — comfort so thin it's almost worse than none.

from A straightforward English compound, cold modifying comfort, in use since at least the late medieval period — Shakespeare used the phrase itself in King John. The logic is plain: real comfort should warm you, so comfort described as 'cold' is comfort drained of the thing that makes it work, like a fire that's gone out.