Many of the island state's highways and schools were closed as heavy snow fell across the state, in some places down to sea level.

The Bureau of Meteorology said a very cold south-westerly airstream had brought the snowfalls, which fell on homes across the state for the first time in a decade.

Police warned against driving on a string of icy roads, and the weather halted fishers at the opening of the state's trout season, with highland roads buried under metre-deep drifts.

With access to schools disrupted for teachers and students, and ice on school paths, many state and private schools gave their students the day off, according to the state Education Department.

Victorians won't see anything quite so dramatic but the bureau has predicted falls down to 400 metres over Gippsland and 800 metres elsewhere.

Senior forecaster Terry Ryan said the Dandenongs might also see some snowfall before the air warmed up this afternoon.

Snow showers are also forecast down to 800 metres on Tuesday.

The snow kicks off another cold week in Melbourne, with temperatures forecast around 12 and 13 until the week's high of 15 on Sunday.

Mr Ryan said the week followed the coldest July since 1995 (an average of 13.3 degrees).

This compares to a relatively balmy 19 and 20 degrees at the end of July last year.

"Winter is hanging on," Mr Ryan said.