Recently, a series of oxyfluorides, Sr1−xBaxFeO2F with x = 0, 0.25, 0.50, and 0.75 obtained through a novel synthesis route, were characterized by X-ray and neutron powder diffraction (NPD), magnetization measurements, and 57Fe Mössbauer spectroscopy (MS). The diffraction data revealed random occupancy of Sr and Ba atoms at the A-cation site, and a statistical distribution of O and F at the anionic sublattice of the perovskite-like structure specified in space group Pm-3m. MS spectra analysis consistently indicated the presence of Fe3+ ions at B-site, confirming the Sr1−xBaxFeO2F stoichiometry. Magnetic structure determination from the NPD data at room temperature established G-type antiferromagnetic arrangement in all compositions with Fe3+ moments of about 3.5 μB oriented along the c axis. In this study, we present and analyze additional NPD data concerning the low-temperature chemical and magnetic structure of Sr0.5Ba0.5FeO2F (x = 0.5) and SrFeO2F (x = 0). Basically, the three-dimensional G-type magnetic structure is maintained down to 2 K, where it is fully developed with an ordered magnetic moment of 4.25(5) μB/Fe at this temperature for x = 0.5 and 4.14(3) μB/Fe for x = 0. The data processing is complemented with a new approach to analyze the temperature dependence of the magnetic order TN on the lattice parameters, based on the magnetic hyperfine fields extracted from the temperature-dependent MS data.