TF2 - Moving a hat with part of the face

Is it possible to link a model of a moustache/beard hat to move with a TF2 character’s chin/upper lip?

I’m not sure if the faces are rigged with bones or whatever, but could you just copy a bone out of the face model and link it to a piece of a hat?

At the moment, this is not possible. The various emotions the characters express are created through flexes, not bones, and thus a moustache cannot be rigged to move with the character’s mouth.

Thanks for the quick answer.