  We study the impact of nuclear effects on the extraction of the weak-mixing
angle $\sin^2\theta_W$ from deep inelastic (anti-)neutrino-nucleus scattering,
with special emphasis on the recently announced NuTeV Collaboration 3$\sigma$
deviation of $\sin^2\theta_W$ from its standard model value. We have found that
nuclear effects, which are very important in electromagnetic deep inelastic
scattering (DIS), are quite small in weak charged current DIS. In neutral
current DIS processes, which contain the weak mixing angle, we predict that
these effects play also an important role and may dramatically affect the value
of $\sin^2\theta_W$ extracted from the experimental data.
