Throughout the Rosetta mission, cold electrons (<1 eV) were measured in the coma of comet 67P/Churyumov-Gerasimenko. Cometary electrons are produced at ~10 eV through photoionization or through electron-impact ionization collisions. The cold electron population is formed by cooling the warm population through inelastic electron-neutral collisions. Assuming radial electron outflow, electrons are collisional with the neutral gas coma below the electron exobase, which only formed above the comet surface in near-perihelion high-outgassing conditions (Q > 3 × 10²⁷ s^-1). However, the cold population was identified at low outgassing (Q < 10²⁶ s^-1), when the inner coma was not expected to be collisional. We examine cooling of electrons at a weakly outgassing comet, using a 3D collisional model of electrons at a comet. Electron paths are extended by trapping in an ambipolar electric field and by gyration around magnetic field lines. This increases the probability of electrons undergoing inelastic collisions with the coma and becoming cold. We demonstrate that a cold electron population can be formed and sustained, under weak outgassing conditions (Q = 10²⁶ s^-1), once 3D electron dynamics are accounted for. Cold electrons are produced in the inner coma through electron-neutral collisions and transported tailwards by an E × B drift We quantify the efficiency of trapping in driving electron cooling, with trajectories typically 100 times longer than expected from ballistic radial outflow. Based on collisional simulations, we define an estimate for a region where a cold electron population can form, bounded by an electron cooling exobase. This estimate agrees well with cold electron measurements from the Rosetta Plasma Consortium.