Context : Analysis of all-sky Planck submillimetre observations and the IRAS 100 \mu m 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 examine the SEDs at large scales using IRAS , Planck , and Herschel data .
At smaller scales , we compare with JCMT/SCUBA-2 850 \mu m maps with Herschel data that are filtered using the SCUBA-2 pipeline .
Clumps are extracted using the Fellwalker method and their spectra are modelled as modified blackbody functions .

Results : According to IRAS and Planck data , most fields have dust colour temperatures T _ { C } \sim 14 - 18 K and opacity spectral index values of \beta = 1.5 - 1.9 .
The clumps/cores identified in SCUBA-2 maps have T \sim 13 K and similar \beta values .
There are some indications of the dust emission spectrum becoming flatter at wavelengths longer than 500 \mu m. In fits involving Planck data , the significance is limited by the uncertainty of the corrections for CO line contamination .
The fits to the SPIRE data give a median \beta value slightly above 1.8 .
In the joint SPIRE and SCUBA-2 850 \mu m fits the value decreases to \beta \sim 1.6 .
Most of the observed T - \beta anticorrelation can be explained by noise .

Conclusions : The typical submillimetre opacity spectral index \beta of cold clumps is found to be \sim 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 T - \beta anticorrelation and \beta decreasing at millimetre wavelengths .