The effects of an imposed, axial magnetic field B z0 on hydrodynamics and energetic electrons in inertial confinement fusion (ICF) indirect-drive hohlraums are studied. We present simulations from the radiation-hydrodynamics code HYDRA of a low-adiabat ignition design for the National Ignition Facility (NIF), with and without B z0 = 70 Tesla. The field's main hydrodynamic effect is to significantly reduce electron thermal conduction perpendicular to the field. This results in hotter and less dense plasma on the equator between the capsule and hohlraum wall. The inner laser beams experience less inverse bremsstrahlung absorption before reaching the wall. The x-ray drive is thus stronger from the equator with the imposed field. We study superthermal, or "hot," electron dynamics with the particle-in-cell code ZUMA, using plasma conditions from HYDRA. During the early-time laser picket, hot electrons based on two-plasmon decay in the laser entrance hole (Regan et al. 2010) are guided to the capsule by a 70 T field. 12x more energy deposits in the deuterium-tritium (DT) fuel. For plasma conditions early in peak laser power, we present mono-energetic test-case studies with ZUMA as well as sources based on inner-beam stimulated Raman scattering. The effect of the field on DT deposition depends strongly on the source location, namely whether hot electrons are generated on field lines that connect to the capsule.