"Precipitation: New snow over permafrost.

Still, the permafrost seems to be melting."

You appear to be confusing some terms.

First, Glaciers are made from precipitation- snowfall builds up year after year forming glaciers. For instance if it snows 10' in one year and 5' of it melts but other 5' remains and the next year 5' more is added which also doesn't melt, that is the process that forms a glacier- the snow can later compact into ice [i.e. allowing one to get ice cores].

Permafrost refers to soil that remains frozen throughout the year- nothing to do with glaciers. Now, you can have permafrost areas which partially melts. For example one could walking through an area which has permafrost and be knee deep in mud- it might be waist deep if not for the fact that there is permafrost. The knee deep mud, is not permafrost- obviously, because it has melted. Though years ago it might have been permafrost.