Based on my very basic understanding of the Johnson noise, it's not just a DC phenomena, but should change with frequency in a system, where there is a frequency dependent, real component to the impedance. I think both the skin effect and eddy current losses contribute to the effective resistance of an inductor, so Johnson noise should increase at higher frequencies. Am I being dumb?
As stated in the comments, any loss in the system will contribute to the Johnson noise, so you are right about the skin effect and the Eddy current.
I want to add that, interestingly enough, this apply not only to electric circuits, but to other linear dissipative systems. A very interesting paper from 1951, Irreversibility and Generalized Noise, proves it and provides the following examples:
- Brownian motion
- Dipole radiation
- Acoustic radiation in a gas
I am a electronic engineer, and I stumbled upon this fact while designing a circuit interface for a CMUT, a very low-noise capacitive transducer. As it turns out, the model for such a transducer can be used to predict the electric noise coming from it, although electrically the CMUT is only a capacitor. In facts, the real part of the impedance of the device is mostly due to the acoustic media (air, water, oil, and whatnot), because that is where the energy dissipation happens.