Context. Within the project Galactic cold cores we are carrying out Herschel photometric observations of cold interstellar clouds detected with the Planck satellite. The three fields observed as part of the Herschel science demonstration phase (SDP) provided the first glimpse into the nature of these sources. The aim of the project is to derive the physical properties of the full cold core population revealed by Planck. Aims. We examine the properties of the dust emission within the three fields observed during the SDP. We determine the dust sub-millimetre opacity, look for signs of spatial variations in the dust spectral index, and estimate how the apparent variations of the parameters could be affected by different sources of uncertaint...