Asked by Alan
This is a very interesting question and the subject of much ongoing research. The current hypothesis is that most major ice sheets had lakes beneath them, and current work is attempting to find evidence of these in the geological record, for example, underneath the last British-Irish Ice Sheet.
In terms of smaller valley glaciers, for example, in the Alps, it would depend on their thermal regime, size, and the availability of bedrock basins and topographic lows in which water could accumulate.