The incident occurred in the morning as the man was driving the snow cat over the snow-covered surface of the lake in the bay of Surlej, below slopes of ski resort (Corvatsch), Graubünden cantonal police said.
He was grooming a cross-country ski trail when the vehicle plunged into the lake.
Police divers were able to quickly retrieve the driver and revived him on the spot before putting him in a helicopter for transport to a clinic in Lugano in the canton of Ticino.
He died in the clinic about an hour after arrival, police said.
The grooming machine ended up on the lake bottom at a depth of 54 metres.
Police said an operation to retrieve the vehicle will be organized by police divers in the coming days.
The victim was a municipal employee, the Blick newspaper reported.
The newspaper noted that the grooming machine did not use floats, which are sometimes attached to such vehicles operating on snow- and ice-covered lakes .
Late last month, a snow groomer (known as a PistenBully) broke through the ice at Lake Saint Moritz but the vehicle did not sink because of floats, Blick said.
Police are further investigating Wednesday’s accident.