We have performed polarized and unpolarized small angle neutron scattering experiments on single crystals of HoMnO₃ and have found that an increase in magnetic scattering at low momentum transfers begins upon cooling through temperatures close to the spin reorientation transition at T_SR ≈ 40  K. We attribute the increase to an uncompensated magnetization arising within antiferromagnetic domain walls. Polarized neutron scattering experiments performed while applying an electric field show that the field suppresses magnetic scattering below T ≈ 50  K, indicating that the electric field affects the magnetization via the antiferromagnetic domain walls rather than through a change to the bulk magnetic order.