Sea ice expels salt during ice growth and melt. The expulsion of this dense brine not only impacts the underlying ocean stratification, it also alters the sea ice thermodynamic and microstructural properties and so feeds back on the ice evolution. In addition, modeling sea ice brine dynamics in a global sea ice model such as CICE (the Los Alamos sea ice model), paves the way for ice biogeochemical modeling in coupled climate applications. One of the most challenging sea ice environments to model is the Weddell Sea during the winter-spring transition. Here sea ice evolves through three dynamical regimes: 1) a cold, growth phase where an internal, gravity driven instability governs desalination; 2) a period of heavy snow accumulation which forces the ice deeper into ocean waters and drives brine upwards into the snow layer; and 3) a melt phase during which snow and ice melt percolates downwards, flushing the ice of salt in the process. We incorporate all three processes in a halodynamic version of CICE and simulations compare favorably with field observations from a Weddell Sea field campaign of the Ice Station POLarstern. Notably, as the ice warms, a fresh upper-ice layer forms and the high salinity upper ice layer migrates downward. This simulated pattern is consistent with the early spring development stages of high-porosity layers often observed in Antarctic sea ice and associated with rich biological production.