Globally Sea ice isnt a problem re global warming, the Antarctic ice field is another matter entirely.
Locally the loss of the Arctic sea ice is a major issue as it's looks like it could pull the North Atlantic Conveyor current much further South and deprive us of the moderating effect on our climate giving us a similar climate as other places at our latitude.
The loss of sea ice is actually a problem for global warming, as ice reflects more of the sun's heat than the seawater that replaces it. This is a major effect of sea ice loss.
The North Atlantic Conveyor is driven by deep water formation, where cold, dense water sinks to the bottom of the Atlantic. It's affected by the influx of fresh water which inhibits the process - that's not just from melting sea ice but a larger contribution comes from melting permafrost in Siberia.
Deep water formation, and the Gulf strream that it drives, have shut down before, quite often: they can be seen in the paleoclimate records. The effect is profound. The last time it happened (11 000 years ago, the Younger Dryas), the whole of the northern hemisphere reverted to periglacial conditions. The UK which had been temperate grasslands became tundra in the space of a few decades. It's probably something that we want to avoid!