You say "It all melts", and then "I trust that the experts know the difference between permanent snow....".
I hypothesised satellite photos, I'm not sure if depth of snow is relevant for more than just volume, and whether you could get good estimates of depth (and density???) from a satellite.
Don't forget that modern satellites are topographical with a high degree of accuracy. We can use satellites to learn snowpack depth.
This is how we know that the aquifers are depleted because the satellites measure elevation above the aquifer.