At present, the smallest spot size which can be achieved with state-of-the-art focused ion beam (FIB) technology is mainly limited by the chromatic aberrations associated with the 4.5 eV energy spread of the liquid-metal ion source. Here we numerically investigate the performance of an ultracold ion source which has the potential for generating ion beams which combine high brightness with small energy spread. The source is based on creating very cold ion beams by near-threshold photoionization of a laser-cooled and trapped atomic gas. We present ab initio numerical calculations of the generation of ultracold beams in a realistic acceleration field and including all Coulomb interactions, i.e., both space charge effects and statistical Coulomb effects. These simulations demonstrate that with existing technology reduced brightness values exceeding 105 A m-2 sr-1 V-1 are feasible at an energy spread as low as 0.1 eV. The estimated spot size of the ultracold ion source in a FIB instrument ranges from 10 nm at a current of 100 pA to 0.8 nm at 1 pA.