The simple answer is that the question is bad, because the halocline can only disappear when there is no ice, or a current appears where previously one didn't exist. Extreme storms may mix the upper 60 meters or so, but the salt increase of new forming ice will happen until no new ice forms, and the salt dilution of melting ice will happen until there is no ice to melt all year round, i.e. winter ice free Arctic Ocean as well.
Now, unless a massive current appears which flushes across the Arctic Ocean via input from the Atlantic Ocean, and I don't have any numbers on sverdrups or how many sverdrups go through all the ocean's currents each year, but to me that would seem to me quite impossible and so there will be winter sea ice for a long time.
Here are several maps depicting how deep the mixed layer (that is, the surface layer with identical characteristics throughout its entire depth) is throughout the year:
http://s1.postimg.org/f1qylntkv/Mixed_Layer_Depth.gifhttps://upload.wikimedia.org/wikipedia/commons/c/c7/Mixed_layer_depth.pngIn the second one, the months are January and July. You can see that melting ice, most visible in the Antarctic, as well as summer heating, decreases the depth of the mixed layer.
Now, there is also the fact that we have sea ice, however thin, formed in the region between FJL and Svalbard, which according to HYCOM is over 34ppt saltiness. The main thing to note about the link is that the salinity rises in winter as brine leaks out of FYI forming and falls in summer as the FYI melts back into the Ocean. This will continue even after the first ice-free Arctic Ocean happens, as ice does not need ice to grow back on the scale of weather. This can be seen in the Baltic Sea, many northern rivers and lakes, and the Sea of Okhotsk.
https://www7320.nrlssc.navy.mil/hycomARC/navo/arcticsss_nowcast_anim365d.gif