Context. The project Galactic Cold Cores has carried out Herschel photometric observations of interstellar clouds where the Planck satellite survey has located cold and compact clumps. The sources represent different stages of cloud evolution from starless clumps to protostellar cores and are located in different Galactic environments. Aims. We examine this sample of 116 Herschel fields to estimate the submillimetre dust opacity and to search for variations that might be attributed to the evolutionary stage of the sources or to environmental factors, including the location within the Galaxy. Methods. The submillimetre dust opacity was derived from Herschel data, and near-infrared observations of the reddening of background stars are converted into near-infrared optical depth. We investigated the systematic errors affecting these parameters and used modelling to correct for the expected biases. The ratio of 250 μm and J band opacities is correlated with the Galactic location and the star formation activity. We searched for local variations in the ratio τ(250 μm)/τ(J) using the correlation plots and opacity ratio maps. Results. We find a median ratio of τ(250 μm) /τ(J) = (1.6 ± 0.2) × 10-3, which is more than three times the mean value reported for the diffuse medium. Assuming an opacity spectral index β = 1.8 instead of β = 2.0, the value would be lower by ~ 30%. No significant systematic variation is detected with Galactocentric distance or with Galactic height. Examination of the τ(250 μm) /τ(J) maps reveals six fields with clear indications of a local increase of submillimetre opacity of up to τ(250 μm) /τ(J) ~ 4 × 10-3 towards the densest clumps. These are all nearby fields with spatially resolved clumps of high column density. Conclusions. We interpret the increase in the far-infrared opacity as a sign of grain growth in the densest and coldest regions of interstellar clouds.