  In this paper we extend the color dipole formalism to the study of leading
neutron production in $e + p \rightarrow e + n + X$ collisions at high energies
and estimate the related observables, which were measured at HERA and may be
analysed in future electron-proton ($ep$) colliders. In particular, we
calculate the Feynman $x_F$ distribution of leading neutrons, which is
expressed in terms of the pion flux and the photon-pion total cross section. In
the color dipole formalism, the photon-pion cross section is described in terms
of the dipole-pion scattering amplitude, which contains information about the
QCD dynamics at high energies and gluon saturation effects. We consider
different models for the scattering amplitude, which have been used to describe
the inclusive and diffractive $ep$ HERA data. Moreover, the model dependence of
our predictions with the description of the pion flux is analysed in detail. We
show that the recently released H1 leading neutron spectra can be reproduced
using the color dipole formalism and that these spectra could help us to
observe more clearly gluon saturation effects in future $ep$ colliders.
