I personally feel that if there is a total or near complete sea ice loss in the Arctic, this might introduce extreme temperature gradients to the region. On the onset of winter darkness, these may generate hurricane force winds that pile up extreme pack ice against the Queen Elizabeth Islands, Nunavut. This then would be combined with open Central Arctic causing huge lake-snow effect dumping that could re-generate new ice shelves as snowfall fuses into such pack ice formations.
This could re-instate - volatile and temporary - new "ice shelves" of quite considerable thickness. For shipping these conditions would be deadly even though the Central Arctic might remain open water deep into mid winter. Fortunately, for this season I cannot see ocean warming sufficient even if all ice were lost, the high temperature gradients and adequate moisture conditions are prerequisite for these ice shelves to form from extreme pack ice development combined to equally massive lake-snow falls.
Maurice Ewing and William Donn of Lamont-Doherty Earth Observatory (LDEO) in Palisades, New York were the last researchers advocating Lake-Snow Effect from insolation as a trigger of the Ice Ages ice sheets (since taken over by Milutin Milanković theory of the slow orbital forcings). The problem with Lake-snow from Arctic warming is that even though the effect is seen intensifying, also the land where snow falls also warms (just like Oren said aptly, that in the end it all melts in the Hudson Bay): the net result being higher spring floods in Siberia, not any ice sheet.
Post-Rio-1992 UN Secretary-General Javier Pérez de Cuéllar authorised the First Nations of Americas Ethnoclimatology Motion to be tabled on the floor of UN General Assembly on the Native American history on Foxe-Laurentide Ice Dome on which issue the UNFCCC update is here (some Asian nations lend support to this case history and WMO gave minor conference funding) which I am quite familiar:
https://www.academia.edu/36396474/United_Nations_General_Assembly_Motion_101292_for_UNFCCCs_Talanoa_Dialogue There is no way for new ice sheet. In above, cause is geothermal lake-snow effect and the project goal is to attain funds to GRIP style ice core to retrieve subglacial carbon for AMS test.
Severe problems will only emerge once Arctic begin to be ice free mid-summer, then above effect may be at the tipping point for subsequent winter darkness - extremely unstable - ice shelving north of Canada. The present season (2020) is luckily one light year away from this awkward tipping point.
@Oren as outrageous bbr claim can be, your response should have come in a post apart..
The Hudson Bay thing is part of bbr's hypothesis on a new ice sheet forming in Northern Canada. It also bursts forth on the Northern hemisphere Snowfall thread from time to time. It is true to say that Hudson Bay has successfully mostly ignored AGW over the years. It is also true to say that it melts out completely without fail.