Why does dirty, soot-covered snow melt faster than clean snow?

The amount of heat received by a body from thermal radiation released by another body depends on the absorption coefficient. For a body covered with black paint, this coefficient is about 1, which means that all the radiation that hits the body is absorbed, the smaller this coefficient, the more heat radiation is reflected. The lighter the body, the lower the coefficient.
It turns out that dirty snow has a darker color, it absorbs more heat radiation and heats up faster, therefore it melts faster.