The figures to look at are the capacity for ice to absorb heat energy from sunshine either clean or dusty or sooty.
Given that Greenland has 1m of snowfall (w.e.) a year there would have to be a lot of dirt in the snow for it to have an effect significant compared to the 1m of snow.
If you find these numbers please link to them.
Various studies have clean snow albedo generally around 0.85 to 0.9, or more, and changing to as low as 0.5 with soot and/or dust. That is a factor of three times or more radiative absorption from getting dirty. I fine layer that diminishes the albedo to 0.7 is invisible except under a microscope or other equipment measuring reflectivity.
How about these:
For just 10 ppb on the surface:
We find evidence that black soot aerosols deposited on Tibetan glaciers have been a significant contributing factor to observed rapid glacier retreat. Reduced black soot emissions, in addition to reduced greenhouse gases, may be required to avoid demise of Himalayan glaciers and retain the benefits of glaciers for seasonal fresh water supplies.
BC concentrations of 10 ng g−1 significantly alter the albedo (reflectivity) of a thick snow layer. The visible albedo of deep fresh snow, about 0.9–0.97, is decreased by 0.01–0.04 by a BC amount of 10 ng g−1 (16, 18), thus increasing absorption (1 minus albedo) of visible radiation by 10–100%, depending on the size and shape of snow crystals and on whether the soot is incorporated within snow crystals or externally mixed
The impact of albedo change is magnified in the spring, at the start of the melt season, because it allows melt to begin earlier. Then, as melting snow tends to retain some aerosols, the surface concentration of black soot increases, and BC becomes even more effective at increasing melt of snow and ice.
Black soot and the survival of Tibetan glaciers
BC has been implicated in previous studies as
potentially disrupting Arctic climate. Clarke and Noone
[1985] found that snow albedos are reduced by 1–3% in
fresh snow and by another factor of 3 as the snow ages and
the BC becomes more concentrated.
Distant origins of Arctic black carbon: A Goddard Institute for Space Studies ModelE experiment
This is probably another reason we see a net ice loss in Antarctica and Greenland, but in the arctic:
BC deposition in Greenland is about 10 times greater than in Antarctica and 10 times less than in Tibet.
In addition to absorbing radiation when lofted in the
atmosphere, BC also causes surface warming when deposited
on snow and ice surfaces [Flanner et al., 2007; Hansen and
Nazarenko, 2004]. Sensitive regions (e.g., the Arctic and
the Himalayas) are particularly vulnerable to warming due
to the snow albedo effect [Kopacz et al., 2011; McConnell,
2010], which tends to enhance snow and ice melting due to
the absorption caused by the increased BC deposition.
Historical and future black carbon deposition on the three ice caps: Ice core measurements and model simulations from 1850 to 2100
I have seen more dramatic numbers than these in other studies, but don't recall the keywords I need to find the studies.
Whether from the sun, or forcing from greenhouse gasses, the snow is warming twice as fast or more from the albedo changes cause by soot.