The superconducting nanowire single-photon detector (SNSPD) is a leading technology for quantum information science applications using photons, and is finding increasing uses in photon-starved classical imaging applications. Critical detector characteristics, such as timing resolution (jitter), reset time, and maximum count rate, are heavily influenced by the readout electronics that sense and amplify the photon detection signal. We describe a readout circuit for SNSPDs using commercial off-the-shelf amplifiers operating at cryogenic temperatures. Our design demonstrates a 35 ps timing resolution and a maximum count rate of over 2 × 10⁷ counts per second, while maintaining <3 mW power consumption per channel, making it suitable for a multichannel readout.