The relaxation of high-energy "hot" carriers in semiconductors is known to involve the redistribution of energy between hot and cold carriers, as well as the transfer of energy from hot carriers to phonons. Over the past few years, these two processes have been identified in lead-halide perovskites (LHPs) using ultrafast pump-probe experiments, but their interplay is not fully understood. Here we present a practical and intuitive kinetic model that accounts for the effects of both hot and cold carriers on carrier relaxation in LHPs. We apply this model to describe the dynamics of hot carriers in bulk and nanocrystalline CsPbBr3 as observed by multi-pulse "pump-push-probe" spectroscopy. The model captures the slowing of the relaxation dynamics in the materials as the number of hot carriers increases, which has previously been explained by a "hot-phonon bottleneck" mechanism. The model also correctly predicts an acceleration of the relaxation kinetics as the number of cold carriers in the samples is increased. Using a series of natural approximations, we reduce our model to a simple form containing terms for the carrier-carrier and carrier-phonon interactions. The model can be instrumental for evaluating the details of carrier relaxation and carrier-phonon couplings in LHPs and other soft optoelectronic materials.