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When it rains, only the compressed snow is left
(feddit.uk)
Desire paths Desire paths can be paths created as a consequence of erosion caused by human or animal foot-fall or traffic. The paths usually represent the shortest or most easily navigated routes between origins and destinations. https://en.wikipedia.org/wiki/Desire_path
People walking on the snow will compact it down, eventually forming an ice layer. Rain is much better at melting snow than ice, so these paths can remain as the snow melts during/after rain.