The Arctic Ice Pack grows very slowly, because prevailing winds have already lost their moisture long before getting to the Arctic Circle. Since it doesn’t melt at all during most of the year, the balance is better than it might be, but for a long time now, it has not been growing. In historic times, it has been shrinking, and that process may well be approaching speeds that will cause a catastrophic melting. (Catastrophic meaning happening in mere centuries, rather than millennia.)
The point is that snow falling onto the open ocean is not going to form an Ice Pack under normal conditions. The current Arctic Ice Pack originated on the land surrounding the Arctic sea, and grew out as shelves from all around, during the million year period that is the current Ice Age. During the various interglacial periods, much of the ice at the margins has been melting, but the polar region has remained frozen, although becoming thinner at times.
Once it actually melts the situation changes. While more snow will form, that snow must accumulate along the frozen areas south of the pole, and then grow out onto the Arctic Sea again. That process might take another million years. It must certainly take longer than breaking up and melting the Ice Cap, because that process is greatly aided by convection, and sea currents moving blocks of Ice southward. No such mechanism exists to accumulate ice at the pole itself.
Antarctica has been more stable during the interglacial periods precisely because so much of the ice pack there is on land. If the central portion of the Antarctic Ice Pack should melt catastrophically, the refreezing could take place much more quickly, if conditions change. This scenario has recently been given strong supporting evidence by studies that show that the Last Glacial Maximum in the Northern Hemisphere did not occur at the same time as the LGM for the Southern Hemisphere. The North appears to have thawed out at a much higher rate. It also seems to have been subject to faster fluctuations over the broader scale of interglacial periods. The presence of land at the South Pole is believed by some to have contributed to the existence of the most recent Ice Age. Other Ice Ages might have coincided with the existence of large percentages of land at the poles, but that is not clearly shown, by existing evidence.
“It should be possible to explain the laws of physics to a barmaid.” ~ Albert Einstein ~
“You should see the place where Einstein used to drink!” ~ Triskadecamus ~