Despite the proliferation of mobile devices in various wide-area Internet of Things applications (e.g., smart city, smart farming), current Low-Power Wide-Area Networks (LPWANs) are not designed to effectively support mobile nodes. In this paper, we propose to handle mobility in SNOW (Sensor Network Over White spaces), an LPWAN that operates in the TV white spaces. SNOW supports massive concurrent communication between a base station (BS) and numerous low-power nodes through a distributed implementation of OFDM. In SNOW, inter-carrier interference (ICI) is more pronounced under mobility due to its OFDM based design. Geospatial variation of white spaces also raises challenges in both intra- and inter-network mobility as the low-power nodes are not equipped to determine white spaces. To handle mobility impacts on ICI, we propose a dynamic carrier frequency offset estimation and compensation technique which takes into account Doppler shifts without requiring to know the speed of the nodes. We also propose to circumvent the mobility impacts on geospatial variation of white space through a mobility-aware spectrum assignment to nodes. To enable mobility of the nodes across different SNOWs, we propose an efficient handoff management through a fast and energy-efficient BS discovery and quick association with the BS by combining time and frequency domain energy-sensing. Experiments through SNOW deployments in a large metropolitan city and indoors show that our proposed approaches enable mobility across multiple different SNOWs and provide robustness in terms of reliability, latency, and energy consumption under mobility.