Glaciers affect global circulation by cooling the air around them. Two major physical systems cause our weather:

1-- Our planet spins as we orbit the sun which causes the air masses to move and
2-- Warmer air masses rise while cooler air masses sink.

Air at the equator is usually much warmer because it is being heated by the direct sun rays. Air at our poles is much cooler. The temperature of the air masses changes how they move and mix.

Glaciers are very cold so they cool the air that flows over them. Sometimes very large glaciers even have their own regulated miniature weather systems!

Without the glaciers cooling the air around them, the air currents in that area would change.

Good question. Antarctica probably won't affect that much because Antarctica is likely to remain cold enough that only a few of its glaciers will melt. Greenland is much more of a wild-card and we really don't know what the end effects of that will be.