Recently, time-of-flight LiDAR using the single-photon detection approach has emerged as a potential solution for three-dimensional imaging in challenging measurement scenarios, such as over distances of many kilometres. The high sensitivity and picosecond timing resolution afforded by single-photon detection offers high-resolution depth profiling of remote, complex scenes while maintaining low power optical illumination. These properties are ideal for imaging in highly scattering environments such as through atmospheric obscurants, for example fog and smoke. In this paper we present the reconstruction of depth profiles of moving objects through high levels of obscurant equivalent to five attenuation lengths between transceiver and target at stand-off distances up to 150 m. We used a robust statistically based processing algorithm designed for the real time reconstruction of single-photon data obtained in the presence of atmospheric obscurant, including providing uncertainty estimates in the depth reconstruction. This demonstration of real-time 3D reconstruction of moving scenes points a way forward for high-resolution imaging from mobile platforms in degraded visual environments.