The by far strongest bound on the sum of the neutrino masses today comes from cosmological observations. Future surveys promise to even tighten this bound significantly and will be realized within the next decade. It is therefore crucial to be aware of parameter degeneracies and the main assumptions hiding behind the cosmological mass bound. We study the impact of non-standard momentum distributions of cosmic neutrinos on the anisotropy spectrum of the cosmic microwave background and the matter power spectrum of the large scale structure. We show that the neutrino distribution has almost no unique observable imprint, as it is almost entirely degenerate with the the neutrino mass and the effective number of neutrino flavours. Performing a Markov chain Monte Carlo analysis with current cosmological data, we demonstrate that the neutrino mass bound therefore heavily depends on the assumed momentum distribution of relic neutrinos.