We theoretically and experimentally studied quantum microwave electrometry in a cold atomic system using Rydberg electromagnetic induction transparency (EIT) and Autler--Townes splitting ( EIT-AT splitting). In cold atoms, a spectral linewidth of ~ 500 kHz for EIT was achieved owing to a significant reduction in residual Doppler width, i.e., by at least an order of magnitude, compared to that in vapor cells at room temperature. Therefore, the minimum microwave electric field intensity EMW that can be measured is 430 μV/cm, which is one order higher sensitivity in the EIT-AT regime than that in vapor cells at room temperature. Unlike microwave electrometry in atomic vapor cells, EIT-AT splitting cannot be observed if EMW is so large that the EIT-AT splitting interval Δ fm exceeds the absorption peak width of the cold atom while scanning the frequency of the probe laser (ωp). Moreover, EIT-AT splitting can be observed if Δ fm exceeds the natural linewidth Γeg of the intermediate states while scanning the coupling laser (ωc) and maintains a high spectral resolution with a high signal-to-noise ratio. While scanning ωc, the upper microwave electric field intensity is limited by the scanning range of our setup. Using our system, we measure the maximum field to be 21.6 mV/cm, nearly three times higher than that of 6.8 mV/cm while scanning ωp. The results indicate that the linear range of EMW measured using EIT-AT splitting considerably improves in cold Rydberg atoms.