  Cross sections for inclusive neutrino scattering off deuteron induced by
neutral and charge-changing weak currents are calculated from threshold up to
150 MeV energies in a chiral effective field theory including high orders in
the power counting. Contributions beyond leading order (LO) in the weak current
are found to be small, and increase the cross sections obtained with the LO
transition operators by a couple of percent over the whole energy range
(0--150) MeV. The cutoff dependence is negligible, and the predicted cross
sections are within $\sim 2$\% of, albeit consistently larger than,
corresponding predictions obtained in conventional meson-exchange frameworks.
