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Wouldn't that cause it to melt faster?

The better the top layer is insulated, the less heat from sunlight dissipates into the cold glacier and stone beneath. This means that the same amount of absorbed heat brings more of the top layer to the melting point than in a less insulated situation. Once the snow has melted it will go back to the old rate, but 22 days of delay would be optimistic.

Assuming the albedo is the same. If the glaciers are grey from dust and debris, then fresh snow will probably increase the reflectivity, which means less sunlight is absorbed as heat, which would cause the snow to last longer. So maybe 22 days of delay would be pessimistic. Or the effects might cancel out.

I don't know if the infrared and air-to-material heat conduction properties of glacier ice and snow are very different. It's probably less significant than albedo and insulation.

So my guess as an amateur physics grad is that during a heat wave (where air-to-material conduction is the primary driver), snow would melt faster than glacier ice, while during a typical preindustrial arctic early spring (where absorption of sunlight is the primary driver) snow would melt slower than glacier ice.

tl;dr: climate science hard