Arctic Ocean area 14,056,000 km2

Say, in the winter 10 million sq km ocean freezes more than 1 meter thick. That amount of ice is 10 million km times .001 km is 10,000 cubic km

Ocean water normally freezes into pure water ice, or at least purer water ice. The result of freezing ocean water is that you get cold sea water with a higher salinity which is therefore denser and it falls.

What causes the water flow of the global conveyor belt is not "having" thick arctic polar sea ice, but rather "making" arctic polar sea ice.

Obviously, this is complicated, but in simple terms if you make 10,000 cubic km of polar sea ice then you get somewhere around 10,000 cubic km of colder denser ocean water. [It could be 2 or 4 times as much and perhaps 1/2 as much- the point is it's somewhere around that scale- and the ratio could vary upon such variables as wind speed and/or how inches of ice is created per day, tide flows, and who knows what.]
But the big factors are that with thicker polar ice the cold weather causes slower ice formation. And that open arctic water should create more ice than areas with existing ice.

Generally speaking if 75% of the area of arctic polar ice melts in the arctic ocean during summer and in the winter it freezes back to around "normal" levels in the winter, then this will add more volume to global conveyor belt, compared an arctic polar ice in which 50% melts during the summer and refreezes back to around the "normal" levels during the winter.