  We derive general expressions for the neutrino dispersion relation in a
magnetized plasma with a wide range of temperatures, chemical potentials, and
magnetic field strengths. If the electron and proton chemical potentials
vanish, as in the early Universe, there is no magnetization contribution to the
neutrino refractive index to leading order in the Fermi coupling constant,
contrary to claims in the recent literature. Therefore, as long as the magnetic
field satisfies $B\simleq T^2$, the neutrino refractive index in the early
Universe is dominated by the standard ``non-local term''. If neutrinos are
Dirac particles with magnetic moment $\mu$, then their right-handed components
are thermally populated before the nucleosynthesis epoch by magnetically
induced spin oscillations if $\mu B_0 \agt 10^{-6}\mu_{\rm B}\,{\rm gauss}$,
where $\mu_{\rm B}=e/2m_e$ is the Bohr magneton and $B_0$ is a large-scale
primordial magnetic field at $T_0\approx 1\,\rm MeV$. For a typically expected
random field distribution, even smaller values for $\mu B_0$ would suffice to
thermalize the right-handed Dirac components.
