The low-energy spectra of gamma-ray bursts' (GRBs)prompt emission are closely related to the energy distribution of electrons, which is further regulated by their cooling processes. We develop a numerical code to calculate the evolution of the electron distribution with given initial parameters, in which three cooling processes (i.e., adiabatic, synchrotron, and inverse Compton cooling) and the effect of a decaying magnetic field are coherently considered. A sequence of results is presented by exploring the plausible parameter space for both the fireball and the Poynting flux-dominated regime. Different cooling patterns for the electrons can be identified, and they are featured by a specific dominant cooling mechanism. Our results show that the hardening of the low-energy spectra can be attributed to the dominance of synchrotron self-Compton cooling within the internal shock model or to decaying synchrotron cooling within the Poynting flux-dominated jet scenario. These two mechanisms can be distinguished by observing the hard low-energy spectra of isolated short pulses in some GRBs. The dominance of adiabatic cooling can also lead to hard low-energy spectra when the ejecta is moving at an extreme relativistic speed. The information from the time-resolved low-energy spectra can help to probe the physical characteristics of the GRB ejecta via our numerical results.