Cold and warm are subjectively attributed to sound but anyway very real experience of perceived sound phenomena....
It is a characterisation of the musical timbre of a specific instrument playing in a specific room from a specific audio system, coming also from a specific recording room, which may be perceived wrongly in two different directions of the spectrum frequencies, because of bad electronical design from the recording gear or/and from the listening gear or from very bad rooms embeddings or from the 2...
But People in general prefer between 2 wrongs the least wrong one or the least agressive one, then in general the warm sound is prefered and associated with heart and body, the cold one with the brain . ... Then warm qualify something more human; cold, something more artificial...
But if the audio system is a good one, turntable or dac, S.S. or tubes; if the audio system is rightfully embedded in the house/room, the rendering of the musical specific timbre of an instrument and his perception will be very good, then relatively neutral, nor warm nor cold, because the timbre is not only, a colored-frequencies phenomenon, it is mainly a time-timing- of many sound aspects-events in a specifically acoustically designed recording and listening rooms...
A good room, a recording one or a listening one, must be the more neutral possible for frequencies perception spectrum then the complex timing of events that constitue timbre will be rightly perceived...