  The Galactic Cold Cores (GCC) project has made Herschel observations of
interstellar clouds where Planck detected compact sources of cold dust
emission. Our aim is to characterise the structure of the clumps and their
parent clouds. We also examine the accuracy to which the structure of dense
clumps can be determined from submillimetre data. We use standard statistical
methods to characterise the GCC fields. Clumps are extracted using column
density thresholding and we construct for each field a three-dimensional
radiative transfer (RT) model. These are used to estimate the relative
radiation field intensities, clump stability, and the uncertainty of column
density estimates. We examine the radial column density profiles of the clumps.
In the GCC fields, the structure noise follows the relations previously
established at larger scales. The fractal dimension has no significant
dependence on column density and the values D = 1.25 +- 0.07 are only slightly
lower than in typical molecular clouds. The column density PDFs exhibit large
variations, e.g. in the case of externally compressed clouds. At scales r>0.1
pc, the radial column density distributions of the clouds follow an average
relation of N~r^{-1}. In spite of a great variety of clump morphology, clumps
tend to follow a similar N~r^{-1} relation below r~0.1 pc. RT calculations
indicate only factor of 2.5 variation in the local radiation field intensity.
The fraction of gravitationally bound clumps increases significantly in regions
with A_V > 5 mag but most bound objects appear to be pressure-confined. The GCC
host clouds have statistical properties similar to general molecular clouds.
The gravitational stability, peak column density, and clump orientation are
connected to the cloud background while most other statistics (e.g. D and
radial profiles) are insensitive to the environment.
