We present new photometric data from our Herschel Key Programme, the Dwarf Galaxy Survey (DGS), dedicated to the observation of the gas and dust in 48 low-metallicity environments. They were observed with PACS and SPIRE onboard Herschel at 70,100,160,250,350, and 500 microns. We focus on a systematic comparison of the derived FIR properties (FIR luminosity, dust mass, dust temperature and emissivity index) with more metal-rich galaxies and investigate the detection of a potential submm excess. The data reduction method is adapted for each galaxy to derive the most reliable photometry from the final maps. PACS flux densities are compared with the MIPS 70 and 160 microns bands. We use colour-colour diagrams and modified blackbody fitting procedures to determine the dust properties of the DGS galaxies. We also include galaxies from the Herschel KINGFISH sample, containing more metal-rich environments, totalling 109 galaxies. The location of the DGS galaxies on Herschel colour-colour diagrams highlights the differences in global environments of low-metallicity galaxies. The dust in DGS galaxies is generally warmer than in KINGFISH galaxies (T_DGS~32 K, T_KINGFISH~23 K). The emissivity index, beta, is ~1.7 in the DGS, but metallicity does not make a strong effect on beta. The dust-to-stellar mass ratio is lower in low-metallicity galaxies: M_dust/M_star~0.02% for the DGS vs 0.1% for KINGFISH. Per unit dust mass, dwarf galaxies emit ~6 times more in the FIR than higher metallicity galaxies. Out of the 22 DGS galaxies detected at 500 micron, 41% present an excess in the submm not explained by our dust SED model. The excess mainly appears in lower metallicity galaxies (12+log(O/H) < 8.3), and the strongest excesses are detected in the most metal-poor galaxies. We stress the need for observations longwards of the Herschel wavelengths to detect any submm excess appearing beyond 500 micron.