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If the air and ground temperatures are below 32, the snow on top would have to be colder, and would almost inevitably be the same temp as the ground and/or air.
As for the melting temp of snow, sometimes I wonder. My back yard has a fence a bit over five feet high on the south side, so it casts a shadow that lasts for several months during the winter. Many times after it has snowed and warmed up into the 40's or even 50's, the snow will linger because it gets no sun. I suppose the explanation would be that the snow in the shadow creates a micro-climate, keeping that temperature below freezing, so the snow is slow to melt.