We succeeded in studying the magnetization-reversal process of a large array of in-plane-magnetized ferromagnetic Co disks by using off-specular polarized neutron reflectometry with spin analysis. We observed enhanced intensity in the off-specular scattered intensity at particular angles. The positions of these satellites are correlated to the lateral periodicity of the magnetic disks. The magnetization-reversal process of the dot array could be effectively studied by measuring the magnetic field dependence of the spin-flip and non-spin-flip contributions to the off-specular intensity of the satellites. The measured spin-flip intensities clearly show that the magnetization reversal is dominated by domain-wall movement within the Co dots and not by a uniform rotation of single-domain particles nor by the presence of a vortex-domain state.