  We apply Bayesian methods to study the sensitivity to neutrino masses of a
Galactic supernova neutrino signal. Our procedure makes use of the full
statistics of events and is remarkably independent of astrophysical
assumptions. Present detectors can reach a sensitivity down to $m_\nu \sim 1$
eV. Future megaton detectors can yield up to a factor of two improvement;
however, they will not be competitive with the next generation of tritium
$\beta$-decay and neutrinoless double $\beta$-decay experiments.
