  We investigate the signatures of neutrinos produced in the annihilation of
WIMP dark matter in the Earth, the Sun and at the Galactic centre within the
framework of the Inert Doublet Model and extensions. We consider a dark matter
candidate, that we take to be one of the neutral components of an extra Higgs
doublet, in three distinct mass ranges, which have all been shown previously to
be consistent with both WMAP abundance and direct detection experiments
exclusion limits. Specifically, we consider a light WIMP with mass between 4
and 8 GeV (low), a WIMP with mass around 60-70 GeV (middle) and a heavy WIMP
with mass above 500 GeV (high). In the first case, we show that capture in the
Sun may be constrained using Super-Kamiokande data. In the last two cases, we
argue that indirect detection through neutrinos is challenging but not
altogether excluded. For middle masses, we try to make the most benefit of the
proximity of the so-called 'iron resonance' that might enhance the capture of
the dark matter candidate by the Earth. The signal from the Earth is further
enhanced if light right-handed Majorana neutrinos are introduced, in which case
the scalar dark matter candidate may annihilate into pairs of mono-energetic
neutrinos. In the case of high masses, detection of neutrinos from the Galactic
centre might be possible, provided the dark matter abundance is substantially
boosted.
