The freezing of water around immersed unfinned and finned horizontal tubes is simulated numerically. The impact of natural convection as well as the water density inversion with temperature is considered. The equations governing both fluid flow and heat transfer around the tubes and through the solid–liquid interface are solved using finite difference schemes. To follow the moving solid–liquid boundary, dynamic grid generation is performed using the elliptic partial differential equation method with iterative interpolating smoothing to avoid divergence. For validation, the present results for unfinned tubes are compared with experimental studies reported in the literature. The present numerical simulations are aimed at improving our understanding of the parameters affecting the freezing process around both finned and unfinned tubes. The results showed that the flow patterns are similar in both tube configurations with one main vortex in the liquid region when there is no inversion in the water density. The presence of fins complicates the distribution of local Nusselt number along the solid–liquid interface in comparison with the unfinned tube. The impact of natural convection on the rate of ice formation is limited to the initial period of the freezing process. The results also show the freezing enhancement when utilizing fins. An accumulated ice mass correlation is developed for each tube configuration. This model can be used to optimize the design of both finned and unfinned tubes in energy storage systems, which are viable tools for air conditioning load shifting and leveling.