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Do the old maps give the light pollution when there is snow on the ground? Short answer: No.

One might think that at least the original light pollution atlas gives the light pollution during those times of the year when there is snow on the ground. However, as first noted by Sky & Telescope editor, Tony Flanders, in this Cloudy Nights thread, the original atlas is overestimating the light pollution when there is snow on the ground as well. Within the context of the model used to calculate the light pollution atlas, you can even calculate the amount that the original light pollution atlas over-estimates the light pollution. In the figure and text below, I compare the light pollution due to a single source of light with snow and without snow cover:

The original light polution model has the albedo of the ground as a parameter, so changing this from the default setting to a snow-like setting will give the effect of snow. 

The albedo of snow is: 
Fresh snow, dry = 0.85 
Fresh snow, wet = 0.80 
Old snow, dry, clean = 0.70 
Old snow, wet, clean = 0.60 
Old snow, wet, medium dirty = 0.50 
Old snow, wet, heavily dirty = 0.40 

I used the new wet snow (0.80) and the old, wet, clean snow (0.60). The effect of snow in "reality" (i.e. the light pollution model, but properly taking into account the reflectivity of snow) with these parameter settings is given by the purple and blue curves in the figure below. The snow effect is largest closest to the source, and decreases to about 25% larger at a distance of 300km. 

If the satellite predominantly measures light directed nearly straight up, then it is measuring mostly reflected light. To make the light pollution map from a satellite, you use this "straight up" light as a proxy for the light in all directions. If you assume the wrong surface albedo (which is what you do if you apply an asphalt/concrete albedo to snow covered ground (as in the original atlas)), then you essentially multiply all the light by a certain factor independent of direction. This is unlike reality, where snow only changes the reflected component. The factor that you wrongly apply to all light is simply the albedo of snow divided by default, asphalt/concrete albedo (=0.15). The effect of snow wrongly estimated from the satellite is shown by the red and orange lines. 

So, the original light pollution atlas is not very useful even when there is snow on the ground. For example, if the snow albedo is 0.6, the orignal light pollution atlas increases the light pollution by a factor of 4 everywhere (= 1.3 light pollution zones). In reality, the effect of snow is more like the blue curve, which is a factor of 1.7 at 30km (= 0.5 light pollution zones) and smaller for greater distnces. If, on the other hand, you do take into account the snow albedo, then the satellite data shoud correctly recover the blue and purple curves. 

(For a point source, the blue and purple curves would go up to the orange and red at very close distances. The source here has a finite size.)