Are tubes really “warm”?

Audio terms like warm are relative. Tubes are in general warm relative to solid state. But you have to watch out, because not only warm but a lot of other terms are used as if they're absolute. They're not. They're relative. You may well be like me and consider your tube gear neutral. But to the average audiophile neutral pretty much means it must be solid state. Which if you ask them pretty much always comes down to them retreating to the sanctuary of measured performance. Which is dumb because there is no oscilloscope, graph or microphone ever made that's calibrated to measure "warm". (They don't measure "neutral", or "transparent" either.) But there you go.

It all depends on the type of tube and it's implementation as you surely know. Warm to me means mid to upper bass emphasis or "dark" An EL34 can sound "warm" Tube sound to me means natural tone and body; two things I really like.

This old adage goes back to when most amps were tube-based and used in systems with limited frequency response. Components like carbon resistors, saggy resistor voltage droppers, and tube rectifiers contributed to this ’tone’ of a rolled off upper treble and woolly bass.
In reality, a good modern tube amp has a certain naturalness which can be attributed to lack of solid state transistor haze caused by switching noise and its associated odd-order harmonic distortion. With modern components, tube amps can sound as cool and neutral as you prefer. Conversely, many solid state amplifiers can  sound warm so it’s not a predictable way to classify the type of sound you’re going to get from a specific type of amplifier. To add complexity to the issue, electronic passive component and tube type, configuration and brand selection can also affect how warm or cool an amplifier sounds. 

Of course if you’re going to play CDs with them it doesn’t really matter since CDs are lacking in warmth and air anyway. You can’t turn a pig’s ear into a silk purse. 🐷