  Context. he study of prestellar cores is essential to understanding the
initial stages of star formation. With $Herschel$ more cold clumps have been
detected than ever before. For this study we have selected 21 cold clumps from
20 $Herschel$ fields observed as a follow-up on original $Planck$ detections.
We have observed these clumps in $^{13}$CO (1-0), C$^{18}$O (1-0), and
N$_2$H$^+$ (1-0) lines. Aims. Our aim is to find out if these cold clumps are
prestellar. We have examined to what extent independent analysis of the dust
and the molecular lines lead to similar conclusions about the masses of these
objects. Methods. We calculate the clump masses and densities from the dust
continuum and molecular line observations and compare these to each other and
to the virial and Bonnor-Ebert masses calculated for each clump. Finally we
examine two of the fields with radiative transfer models to estimate CO
abundances. Results. When excitation temperatures could be estimated, the
column densities derived from molecular line observations were comparable to
those from dust continuum data. The median column density estimates are
4.2$\times 10^{21}$cm$^{-2}$ and 5.5$\times 10^{21}$cm$^{-2}$ for the line and
dust emission data, respectively. The calculated abundances, column densities,
volume densities, and masses all have large uncertainties and one must be
careful when drawing conclusions. Abundance of $^{13}$CO was found in modeling
the two clumps in the field G131.65$+$9.75 to be close to the usual value of
10$^{-6}$. The abundance ratio of $^{13}$CO and C$^{18}$O was $\sim$10.
Molecular abundances could only be estimated with modeling, relying on dust
column density data. Conclusions. The results indicate that most cold clumps,
even those with dust color temperatures close to 11 K, are not necessarily
prestellar.
