  Motivated by a recently found interesting property of the dark halo surface
density within a radius, $r_{\rm max}$, giving the maximum circular velocity,
$V_{\rm max}$, we investigate it for dark halos of the Milky Way's and
Andromeda's dwarf satellites based on cosmological simulations. We select and
analyze the simulated subhalos associated with Milky Way-sized dark halos and
find that the values of their surface densities, $\Sigma_{V_{\rm max}}$, are in
good agreement with those for the observed dwarf spheroidal satellites even
without employing any fitting procedures. This implies that this surface
density would not be largely affected by any baryonic feedbacks and thus
universal. Moreover, all subhalos on the small scales of dwarf satellites are
expected to obey the relation $\Sigma_{V_{\rm max}}\propto V_{\rm max}$,
irrespective of differences in their orbital evolutions, host halo properties,
and observed redshifts. Therefore, we find that the universal scaling relation
for dark halos on dwarf galaxy mass scales surely exists and provides us
important clues to understanding fundamental properties of dark halos. We also
investigate orbital and dynamical evolutions of subhalos to understand the
origin of this universal dark halo relation and find that most of subhalos
evolve generally along the $r_{\rm max}\propto V_{\rm max}$ sequence, even
though these subhalos have undergone different histories of mass assembly and
tidal stripping. This sequence, therefore, should be the key feature to
understand the nature of the universality of $\Sigma_{V_{\rm max}}$.
