  We study a sample of 17 z>1.5 absorbers selected based on the presence of
strong CI absorption lines in SDSS spectra and observed with the ESO-VLT
spectrograph X-shooter. We derive metallicities, depletion onto dust, and
extinction by dust, and analyse the absorption from MgII, MgI, CaII and NaI
that are redshifted into the near infrared wavelength range. We show that most
of these CI absorbers have high metallicity and dust content. We detect nine
CaII absorptions with $W$(CaII$\lambda$3934) >0.23 \AA out of 14 systems where
we have appropriate wavelength coverage. The observed equivalent widths are
similar to what has been measured in other lower redshift surveys of CaII
systems. We detect ten NaI absorptions in the 11 systems where we could observe
this absorption. The median equivalent width ($W$(NaI$\lambda$5891) = 0.68 \AA)
is larger than what is observed in local clouds with similar HI column
densities but also in z<0.7 CaII systems detected in the SDSS. The systematic
presence of NaI absorption in these CI systems strongly suggests that the gas
is neutral and cold, maybe part of the diffuse molecular gas in the ISM of
high-redshift galaxies. Most of the systems (12 out of 17) have
$W$(MgII$\lambda$2796) > 2.5 \AA and six of them have log N(HI) < 20.3, with
the extreme case of J1341+1852 that has log N(HI) = 18.18. The MgII absorptions
are spread over more than $\Delta v$ $\sim$ 400 km s$^{-1}$ for half of the
systems; three absorbers have $\Delta v$ > 500 km s$^{-1}$. The kinematics are
strongly perturbed for most of these systems, which probably do not arise in
quiet disks and must be close to regions with intense star-formation activity
and/or are part of interacting objects. All this suggests that a large fraction
of the cold gas at high redshift arises in disturbed environments.
