We report on the trapping of single Rb atoms in tunable arrays of optical tweezers in a cryogenic environment at $sim 4$ K. We describe the design and construction of the experimental apparatus, based on a custom-made, UHV compatible, closed-cycle cryostat with optical access. We demonstrate the trapping of single atoms in cryogenic arrays of optical tweezers, with lifetimes in excess of $sim6000$ s, despite the fact that the vacuum system has not been baked out. These results open the way to large arrays of single atoms with extended coherence, for applications in large-scale quantum simulation of many-body systems, and more generally in quantum science and technology.