Normal, don't know. Desirable...no. What it shows is that you have a thermal bridge to the outside. Your slab edge insulation should prevent that. Heat goes to cold and you are heating the outdoors. At this point you should look to see if there is any slab edge insulation.

Nope not normal. We have radiant in-floor heat. Never seen any melting outside. Maybe your gutters aren't working right and snow is melting off the roof and melting the snow on the ground?

my understanding is that there is a common fix for this.
excavate around slab to footings, attach foam
sheathing boards to slab, cover with hard surface, like
cement board.

this will eliminate the thermal bypass.

does the snow melt quickly off the roof?
this would be an indication of air leakage
from inside the house leaking into the attic
and/or lack of proper insulation install.

interesting issue. please let us know
what you determine the issue to be &
what your fix will be.

best of luck.