You can verify the current snow status by checking the values reported by the Malga Losch weather station from ARPAV, located close to the battlesite, at the same height and exposition.
Here you can find the weather table for the last 60 days. The graph for yesterday is here reported for convenience:
The Scarpa–Gurekian hut is placed nearby the Malga, and has a beautiful webcam pointing N-E towards the Agordo Valley. It is also a very good indicator of the current amount of snow. This is the last image taken (it might not be updated!):
For more webcam shots from other huts, we highly recommend the RifugInRete site. You’ll also find some images of the last 24h from several huts there, including the Scarpa–Gurekian.
The best short range forecasts are provided by the regional environmental agency ARPAV. See here for the generic Dolomites forecast (PDF) and here for the local one for South-Western Dolomites.
For those you weather nerds, MeteoBlue also produces pretty good 7-day multimodel forecasts as well as meteograms. For the normies, Windy should do: