In this work we have used 3D hydrodynamical (CO5BOLD) and 1D hydrostatic (LHD) stellar atmosphere models to study the importance of convection and horizontal temperature inhomogeneities in stellar abundance work related to late-type giants. We have found that for a number of key elements, such as Na, Mg, Si, Ca, Ti, Fe, Ni, Zn, Ba, Eu, differences in abundances predicted by 3D and 1D models are typically minor (< 0.1 dex) at solar metallicity. However, at [M/H] = -3 they become larger and reach to -0.5...-0.8 dex. In case of neutral atoms and fixed metallicity, the largest abundance differences were obtained for the spectral lines with lowest excitation potential, while for ionized species the largest 3D-1D abundance differences were found for lines of highest excitation potential. The large abundance differences at low metallicity are caused by large horizontal temperature fluctuations and lower mean temperature in the outer layers of the 3D hydrodynamical model compared with its 1D counterpart.