We have developed the first three-dimensional collisional model of electrons at a comet, which we use to examine the impact of electron-neutral collisions in the weakly outgassing regime. The test particle Monte Carlo model uses electric and magnetic fields from a fully kinetic Particle-in-Cell (PiC) model as an input. In our model, electrons originate from the solar wind or from ionisation of the neutral coma, either by electron-impact or absorption of an extreme ultraviolet photon. All relevant electron-neutral collision processes are included in the model including elastic scattering, excitation and ionisation. Trajectories of electrons are validated against analytically known drifts and the stochastic energy degradation used in the model is compared to the continuous slowing down approximation. Macroscopic properties of the solar wind and cometary electron populations, such as density and temperature, are validated with simple known cases and via comparison with the collisionless PiC model. We demonstrate that electrons are trapped close to the nucleus by the ambipolar electric field, causing an increase in the efficiency of electron-neutral collisions. Even at a low outgassing rate (Q = 1026 s−1), electron-neutral collisions are shown to cause significant cooling in the coma. The model also provides a multi-step numerical framework that is used to assess the influence of the electron-to-ion mass ratio, enabling access to electron dynamics with a physical electron mass.