  Taking into account the available accelerator and astrophysical constraints,
the mass of the lightest neutral Higgs boson h in the minimal supersymmetric
extension of the Standard Model with universal soft supersymmetry-breaking
masses (CMSSM) has been estimated to lie between 114 and ~ 130 GeV. Recent data
from ATLAS and CMS hint that m_h ~ 125 GeV, though m_h ~ 119 GeV may still be a
possibility. Here we study the consequences for the parameters of the CMSSM and
direct dark matter detection if the Higgs hint is confirmed, focusing on the
strips in the (m_1/2, m_0) planes for different tan beta and A_0 where the
relic density of the lightest neutralino chi falls within the range of the
cosmological cold dark matter density allowed by WMAP and other experiments. We
find that if m_h ~ 125 GeV focus-point strips would be disfavoured, as would
the low-tan beta stau-chi and stop -chi coannihilation strips, whereas the
stau-chi coannihilation strip at large tan beta and A_0 > 0 would be favoured,
together with its extension to a funnel where rapid annihilation via
direct-channel H/A poles dominates. On the other hand, if m_h ~ 119 GeV more
options would be open. We give parametrizations of WMAP strips with large tan
beta and fixed A_0/m_0 > 0 that include portions compatible with m_h = 125 GeV,
and present predictions for spin-independent elastic dark matter scattering
along these strips. These are generally low for models compatible with m_h =
125 GeV, whereas the XENON100 experiment already excludes some portions of
strips where m_h is smaller.
