Context.Analysis of all-skyPlancksubmillimetre observations and the IRAS 100μm data has led to the detection of a population of Galactic cold clumps. The clumps can be used to study star formation and dust properties in a wide range of Galactic environments.Aims.Our aim is to measure dust spectral energy distribution (SED) variations as a function of the spatial scale and the wavelength.Methods.We examined the SEDs at large scales using IRAS,Planck, andHerscheldata. At smaller scales, we compared JCMT/SCUBA-2 850μm maps withHerscheldata that were filtered using the SCUBA-2 pipeline. Clumps were extracted using the Fellwalker method, and their spectra were modelled as modified blackbody functions.Results.According to IRAS andPlanckdata, most fields have dust colour temperaturesT_C~ 14–18 K and opacity spectral index values ofβ= 1.5–1.9. The clumps and cores identified in SCUBA-2 maps haveT~ 13 K and similarβvalues. There are some indications of the dust emission spectrum becoming flatter at wavelengths longer than 500μm. In fits involvingPlanckdata, the significance is limited by the uncertainty of the corrections for CO line contamination. The fits to the SPIRE data give a medianβvalue that is slightly above 1.8. In the joint SPIRE and SCUBA-2 850μm fits, the value decreases toβ~ 1.6. Most of the observedT-βanticorrelation can be explained by noise.Conclusions.The typical submillimetre opacity spectral indexβof cold clumps is found to be ~1.7. This is above the values of diffuse clouds, but lower than in some previous studies of dense clumps. There is only tentative evidence of aT-βanticorrelation andβdecreasing at millimetre wavelengths.