For melting snow over a burner like that, you need a base. The standard base is a piece of Masonite, at least 8" square or larger, and covered by aluminum foil. The ultralightweight base is cardboard of the same size, and covered by aluminum foil, but it doesn't last for too many days.
The issue is that most of your burner heat hits the melt pot, and then some heat is reflected back down. If all that is there is surface snow, then it is going to melt and tip the burner. If you can get a reflective base in there, then the burner will not tip so easily.