  The experimental data on atmospheric and solar neutrinos are used to test the
framework of non-anomalous Abelian horizontal gauge symmetries with only three
light active neutrinos. We assume that the hierarchy in mass-squared splittings
is not accidental and that the small breaking parameters are not considerably
larger than 0.2. We find that the small angle MSW solution of the solar
neutrino problem can only be accommodated if the $\nu_\mu-\nu_\tau$ mass
hierarchy depends on the charges of at least three sterile neutrinos. The large
angle MSW solution can be accommodated in simpler models if $\nu_e$ and
$\nu_\mu$ form a pseudo-Dirac neutrino, but it is difficult to induce large
enough deviation from maximal mixing. The vacuum oscillation solution can be
accommodated rather simply. We conclude that it is possible to accommodate the
neutrino parameters in the framework of Abelian horizontal symmetries, but it
seems that these parameters by themselves will not provide convincing evidence
for this framework.
