As of now, even the "warm" GFS isn't sending temps into the 40's and obliterating the previous snow. The LSV goes up to 34, maybe 35 tops before the bottom falls out. Rain falling on snow with a temp of 34 is not going to obliterate the new snowpack. The GFS is also notorious for warming things up too much at the surface.
I'm about to see what the ICON is showing for storm #2 and will report back. It's been consistently colder, and now along with its next door neighbor the UKIE.