  We study the role of chiral nuclear forces on the propagation of neutrinos in
hot neutron matter. In particular, we analyze the convergence of the dynamical
structure factor and the neutrino mean free path with the order of the power
counting of the chiral forces, as well as the role of the regulator cut-off of
these forces in the determination of these quantities. Single-particle energies
and chemical potentials needed to calculate the dynamical structure factor are
obtained within the Brueckner--Hartree--Fock approximation extended to finite
temperature. Our results show that the dynamical structure factor and the
neutrino mean free path depend on the cut-off only when the chiral potential is
considered at leading order (LO) and next-to leading order (NLO), becoming this
dependence strongly reduced at higher orders in the chiral power counting due
to the role of three-nucleon forces that start to contribute at next-to-next-to
leading order (N$^2$LO) being, in particular, almost negligible at
next-to-next-to-next-to leading order (N$^3$LO). The neutrino mean free path is
found to converge up to densities slightly below $\sim 0.15$ fm$^{-3}$ when
increasing the order of the chiral power counting, although no signal of
convergence is found for densities above this value. The uncertainty associated
with our order-by-order nuclear many-body calculation of the neutrino mean free
path is roughly estimated from the difference between the results obtained at
N$^2$LO and N$^3$LO, finding that it varies from about a few centimeters at low
densities up to a bit less than $2$ meters at the largest one considered in
this work, $0.3$ fm$^{-3}$.
