I must admit I'm a bit confused when it comes to the halocline and the north-eastern branch of the Gulf Stream that stretches it's fingers all the way to the Arctic Ocean (The North Atlantic Drift).
Several years back I remember reading quite a bit about what drives the Gulf Stream circulation and it's North-Eastern offshoot, and the best explanation I remember was along the lines of there being three main forcings, all of approximately equal importance:
1) Winds blowing mainly towards the North-East over the Atlantic Ocean.
2) Tidal pull from east to west shifts water over the Mid-Atlantic ridge, causing westward movement of deep water. I'm not sure if surface waters are affected, there's an amphidronic point west of Iceland with strong tidal waves moving eastward from there.
3) Cooling and sinking in the far north.
The wind forcing seems to be able to explain fully the main Gulf Stream circulation according to Wikipedia - i.e. it would still be there without the halocline. Wind forcing is also strong towards the North-East along the whole length of the North-Eastern branch of the current, exerting a significant pull.
I'm not so sure about the tidal forcings - perhaps they are insignificant when it comes to driving the Gulf Stream.
The halocline, according to Wikipedia, happens when water evaporates from the surface at mid latitudes, leaving the top layer warmer but saltier than underlying layers and potentially causing vertical instability. But further north, in the Arctic ocean, the reverse seems to be the case - the underlying layers are warmer and saltier than the surface layer, presumably because the warm ocean currents dives under a less saltier lens of cold waters?
The halocline as a driver of ocean currents, on the other hand, as I understand it, is when the ocean freezes, cooling and increasing the salinity of the surface waters, which eventually sink, pulling other surface waters towards the ice-forming region. This is different from point 3 above, where it's only the cooling that causes sinking, not changes in salinity.
Now I may completely have misunderstood the whole thing, hence the "stupid question". But as I understand it, the process of freezing pulls warm surface waters from the south and is at least a local driver of currents. This obviously only works during freezing season (the reverse should be true at other times), and should always pull the warm waters towards the ice edge.
So how will this change over time? If freezing-induced sinking is a pulling force, then the annual amount of pulling should be proportional to the volume of ice freezing? Or is surface freezing more important than thickening later? Is freezing-induced sinking not a positive feedback, in that there presumably is a border line where air temperatures can overcome surface heat, and as the surface warms up due to global warming, this border will shift northwards, pulling the warm waters along with it, delaying ther sinking?
If wind and cooling are the largest forces driving the Gulf Stream, should we be worried about a potential collapse as ocean ice retreats? (Melt-water runoff from Greenland is a different matter).
Now I'm aware that the Gulf Stream has collapsed before, causing the massive temperature swings that can be seen in Greenland ice cores (these cores btw do not measure global temperatures directly, only the surface temperatures of the evaporation zones where the falling snow originates). But these collapses were caused by events vastly bigger in scale than anything on our horizon.
To conclude my ramblings: My understanding of the Gulf Stream and the halocline tells me that a collapse in the Gulf Stream is not imminent, and also, that as sea ice retreats the warm surface waters will seek further and further north, both as a cause and effect.
But even with an all-year ice-free arctic, sinking will always take place due to cooling. Even if the oceans were both totally ice-free and totally salt free, the Gulf Stream would still bring excess warmth from mid latitudes towards the Arctic Ocean.