Good information. Obvious. Never occurred to me before.
Didn't know that, huh?
That's why all the talk is of the Greenland glacier. The Antarctic ice is also sitting on rock, rather than sea water. Other places the tyro might expect big glaciers - like Siberia - don't have any to speak of because the air is too dry by the time it gets there to dump much snow. No snow, no accumulation, no glacier. The ice packs around the edges of Greenland are frozen seawater, and floating. The study of the historical extent of the ice around the Denmark Strait would also be a good measure of average temperature, rather than a measure of snowfall, but, like my proposed study of Baltic ice, has apparently not been done. Iceberg counts would be an indirect measure of average temperature because the usual weather pattern, west-to-east, picks up moisture as the air travels over, mainly, Baffin Bay. Then as it gets to the coast of Greenland it increases in altitude as it flows over the glacier. With increase in altitude, the air temperture and pressure drop, as does the solubility of water in air. Water therefore precipitates out as snow. As long as the surface of Greenland is below freezing, the snow doesn't melt, but is buried by successive snows, eventually compacting to ice.
Ta-da, a glacier. The glacier's own weight causes it to ooze out the edges. As it extends over the edge of the land mass, the edge of the glacier loses its support, and cantilevers out over and into the ocean. At some point it breaks off in chunks, which float away as icebergs. So iceberg activity is an indirect measure of snowfall.
Note that clear evidence that the Greenland ice is still accumulating nicely is not evidence that it's getting thicker - it all depends on whether it's accumulating faster than it's squirting out the sides. Increased snowfall could well be an indicator of higher temperatures, but it rather depends on the rates of accumulation. These can be estimated in some cases from layers in the ice, which are readable like tree rings, if certain assumptions are made, and if the grad students assigned to count layers aren't so politically motivated that they automatically find the proper evidence. The fact that aircraft which landed on the ice during WW2 are now 30 to 50 feet down in ice just tells us that, yes indeed, it's been snowing since then. It's not a direct clue as to temperature, itself.
One complication to this scenario is that everything slows down when open bodies of water like Baffin Bay are mostly iced over, as they are most of the time. Evaporation to the air passing over is then greatly reduced, and so is the subsequent snowfall. And so is the clarity of those annual layers.
A glacier is a dynamic system, depending throughout its life cycle on quite a few factors.