The structures, energies, harmonic vibrational frequencies, and thermodynamic parameters of the water clusters (H2O)48, (H2O)72, and (H2O)270 were calculated using the standard DFT theory (BLYP/6-31++G(d,p) for small and medium clusters) and the modern tight-binding method SCC-DFTB (DFTBA and DFTB+). The adsorption and embedding of s-cis- and s-trans-glyoxal molecules as well as its sunlight UV photolysis products (molecules CH2O, HCOOH, H2O2, CO, CO2 and radicals CHO, HO, HO2) on nanosized ice clusters of up to 2.5 nm in diameter were studied within the above theoretical models. The structures of adsorption complexes on different sites of ice nanoparticles, the corresponding adsorption energies and thermodynamic parameters were estimated. We found that the DFTB method is a very promising tool for the calculations of structures and energies of ice nanoparticles, when compared to both DFT and semiempirical (PM3) methods. The obtained results are discussed in relation to the possible photolysis pathways, the reaction rates in the gas phase and in the adsorbed state, and the mechanisms of glyoxal photolysis catalyzed by the ice nanoparticles in the Earth’s atmosphere.