Sea ice formation is a complex process and is in itself still an active area of research. The turbulence of the ocean and the salinity of the sea water means sea ice forms very differently to that of pure ice.
The salinity of sea water lowers the freezing point of the the water. For the kinds of salinities we find at the ocean surface (34 parts per thousand) we have a freezing temperature of around -1.8 degrees C (pure water freezes at 0 degrees C!). The sea ice then retains some of this salt in brine pockets which significantly affect the thermal properties of the sea ice. Some of this brine is then drained away (mainly through a process of gravity drainage, although other mechanisms play a role too). We always expect the sea ice to maintain some kind of bulk salinity (a rough approximation of 5 parts per thousand are often used in models). Photo of sea ice courtesy of Rosie Willatt, CPOM.