We propose a new astrophysical test on the nature of dark matter based on the properties of dark halos associated with dwarf spheroidal galaxies. The method adopts a mean surface density of a dark halo defined within a radius of maximum circular velocity, which is derivable for a wide variety of galaxies with any dark-matter density profiles. We find that even though dark halo density profiles are derived based on the different assumptions for each galaxy sample, this surface density is generally constant across a wide mass range of galaxy. We find that at higher halo-mass scales, this constancy for real galaxies can be naturally reproduced by both cold and warm dark matter (CDM and WDM) models. However, at low-mass scales, for which we have estimated from the Milky Way and Andromeda dwarf satellites, the mean surface density derived from WDM models largely deviates from the observed constancy, whereas CDM models are in reasonable agreement with observations.