This is a non-trivial issue. When you look at volume change of a glacier, you typically subtract two digital elevation models to obtain the difference between the two. First, you must differentiate between ice sheets where ice berg calving reduces volume and more ordinary glaciers with melt processes. There are of course calving glaciers as well so it is possible to get into great detail for any one specific glacier, so here I will just discuss the most common case which is a smaller glacier with melt-freeze conditions.
The change in elevation differs in magnitude across the glacier surface due to the movement of the glacier and accumulation-melt processes. The surface material can be (1) glacier ice, (2) snow, (3) firn snow that has survived a melt season) or (4) super imposed ice all with more or less differing densities, you need to assess what sort of material has been removed.
Ice can be approximated by a density of 900 kg/m3, firn has a density of about 600 kg/m3 but it must be remembered that the firn is converted to glacier ice by metamorphic processes so that the density changes with depth from 600 to 900 kg/m3. the transition to ice occurs at depths of about 30 m in temperate glaciers although few studies exist on the actual processes that occur. Snow have very differing densities but considering averages, I would say that it would vary between 350 to maybe 500 kg/m3 for winter (cold) conditions and around 550 kg/m3 for a melting snow pack. Super-imposed ice is closer to ice and probably varies in the upper range of 800--900 kg/m3.
To make matters worse, snow superimposes firn which in turn superimposes ice. This means that in the accumulation area, volume change can result from both a reduction in a snow cover and the firn layer. In the zone near the equilibrium line there can be a loss of both firn and ice. this is also where the superimposed ice will play a role.
So there is no simple density to use since the loss you try to estimate will involve varying types of densities spatially as well as vertically. For annual changes, you can largely ignore the vertical distribution, but with volume changes covering larger periods where climate change influences the longer term location of the equilibrium line and the size of the accumulation area, vertical layering also has to be included.
As a first approximation, a surface zonation of ice snow and possibly firn can be used and perhaps lumping snow and firn with a single density of around 600 kg/m3 can be used. I would, however, say that to some extent any choice you make will be wrong, so being aware of complexity and the limitations is the only way forward.
A couple of useful sources relating to the question:
Huss, M., 2013. Density assumptions for converting geodetic glacier volume change to mass change. The Cryosphere [Open Access]
Moholdt, G., (Referee) Interactive comment on “Density assumptions for converting geodetic glacier volume change to mass change” by M. Huss. The Crypshere Discuss. [Open Access]