The snow has blocked all roads and rail links leading to the resort, which lies below the famed Matterhorn mountain, leaving tourists with no means to leaving the area.
Despite the heightened avalanche warning, locals say that by and large, most visitors are fairly unbothered in Zermatt.
"The persons in charge are working hard on the reopening and are confident to open the railway in the afternoon", it added.
Two houses in St Niklaus, near Zermatt, were evacuated on Monday evening.
With temperatures touching 1 deg C, residents in the northern town of Ain Sefra enjoyed sliding down the dunes on Sunday morning, before the snow melted away. Towns and villages across Switzerland, France, and Italy have been cut off due to the extreme winter weather.
The tourism office's website noted a "power breakdown all over Zermatt" and requested people stay at home so not to disrupt those clearing snow.
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A local official in Zermatt, Christian Zioerjen, told AFP that authorities made a decision to resume airlifts once it became clear that train travel had to be pushed back.
Helicopters were flying in fresh laundry for hotels, according to reports.
Italian Alpine resorts were the first to be hit by heavy snowfalls.
One skier was killed and another injured during an avalanche in the French Pyrenees.
Snow and broken branches filled the building's corridors and staircases, but the 29 people who were inside at the time escaped unharmed.
Helicopters have also started to airlift some of the stranded groups away from the resort with the authorities pledging they were in control of the evacuation.
The local police could not be immediately reached for comment.