The authorities said that the freak weather conditions had killed a mother and her 11-year-old daughter on an off-piste ski run in Val Venosta, northwest of Bolzano.
Italy’s Alpine rescue service said the two were rescued alive in critical condition despite “prohibitive” weather conditions but died soon after.
Forecasters at the weather centre in Bolzano put the risk of an avalanche at four on a scale of one to five along the Cresta di Confine on Italy’s border with Austria.
Fears are growing that a dangerous avalanche could leave hundreds at risk, as the weather deteriorates.
Sara Bordet, Commissioner of the Municipality of Valtournenche told Ill Messaggero: “Tomorrow morning as soon as visibility allows it, we will make further assessments with the avalanche commission.”
Ms Bordet, added that the the Civil Protection of Valle d’Aosta were closely monitoring several locations at risk of snowfall.
Cervinia ski authorities announced that the main road leading into Cervinia from Valtournenche was closed in both directions due to possible avalanches.
The authorities warned that Breuil-Cervinia (Aosta), where almost two metres of snow fell, would remain cut off, except for emergency vehicles.
The strong winds from the North-West brought rough weather conditions and snow at high altitudes to Courmayeur, Valsavarenche, Ayas, Rhemes and Oyace.
And the dangerous weather was also affecting Southern Italy.
Local reports suggest that there was widespread travel disruption and traffic in Sicily and the Catania-Messina motorway was blocked by several fallen trees.
In a bid to protect citizens, the mayor of Catania Enzo Bianco ordered the closure of the Bellini Garden and the municipal parks and cemeteries.
In Calabria, rail traffic on the Ionian line stopped twice due to trees uprooted by the wind, causing heavy delays and cancellations for regional and intercity trains.
The Civil Protection of the Prefecture of Reggio Calabria set up a crisis unit to monitor the situation.
In Sardinia, a ferry coming from Livorno to dock at Golfo Aranci was diverted to Olbia.
There was also disruption in Porto Torres, where the Tirrenia motorboat coming from Genoa was about 90 minutes late.
Additional reporting by Maria Ortega