The National Snow and Ice Data Center website describes the process of ice formation on polar oceans. Virtually all of the young ice is made from ocean water which retains some brine in the process of forming. Older ice tends to lose the brine and have it replaced by air bubbles.
Surface ice would form differently, either by frost, which tends to form in patterns or in snow fall. Over many years it might be possible for snowfall and surface forming ice to build up on top of permanent ocean ice. I'm not sure what the ratio could eventually become, but if sea ice was to be mostly from the air, it would need to be very old where over time, enough ice formed on top and the original ice melted from the bottom. On average I suspect most sea ice is ocean ice though, even multi-year ice.
When temperatures are low enough (below -1.8 °C), ice forms naturally in polar ocean-water. See phase diagram: http://antoine.frostburg.edu/chem/senese/101/solutions/images/saltwater-phase-diagram.gif
Salt can freeze along with water in ice below -21 °C, but oceans tend to circulate quite efficiently, so -21 °C water is unlikely in oceans.