Conventional power flow algorithms assume that the network resistances and reactances remain constant regardless of the weather and loading conditions. Although the impact of the weather in power flow analysis has been recently investigated via weather-dependent power flow (WDPF) approaches, the magnetic effects in the core of Aluminum Conductor Steel Reinforced (ACSR) conductors have not been explicitly considered. ACSR conductors are widely used in distribution networks. Therefore, this manuscript proposes a three-phase weather-dependent power flow algorithm for 4wire multi-grounded unbalanced microgrids (MGs), which takes into consideration the impact of weather as well as the magnetic effects in the core of ACSR conductors. It is shown that the magnetic effects in the core can significantly influence the power flow results, especially for networks composed of single-layer ACSR conductors. Furthermore, the proposed algorithm explicitly considers the multi-grounded neutral conductor, thus it can precisely simulate unbalanced low voltage (LV) and medium voltage (MV) networks. In addition, the proposed approach is generic and can be applied in both grid-connected and islanded networks. Simulations conducted in a 25-Bus unbalanced LV microgrid highlight the accuracy and benefit of the proposed approach, while its computation performance is tested in the IEEE 8500-Node network.