The magnetic and structural properties of two-dimensional spatially ordered systems of ferromagnetic nickel nanowires embedded into an Al₂O ₃ matrix have been studied using polarized small-angle neutron scattering (polarized SANS). We measured the total (nuclear and magnetic) scattering I(q) as a polarization-independent scattering, the field-dependent scattering as I_H(q) = I(q, H) - I(q, 0), where H is the magnetic field, and the nuclear-magnetic interference as a polarization-dependent (P) scattering ΔI(q, P). A typical scattering pattern is composed of the diffuse small-angle scattering and the Bragg peak. It is shown that the introduction of Ni into the matrix does not change the position of the Bragg peak but results in an increase of the scattering intensity both in the small-angle region and at the Bragg positions. An external magnetic field was applied perpendicular or parallel to the long dimension of the nanowires in order to reveal the anisotropic properties of the magnetic system. It is shown that, firstly, the magnetic-field-dependent scattering I_H(q) provides new and principally different information as compared with the interference term ΔI(q). Secondly, two contributions to the interference term ΔI(q) (ascribed to the diffuse scattering and to the diffraction peaks) have different signs indicating different origins of the scattering objects. Thirdly, polarized SANS gives a detailed picture of the magnetization process, which could not be obtained by methods of standard magnetometry.