There have been more than 48 requests for emergency assistance in the North and South of the state overnight, the State Emergency Service says.
SES crews responded to calls for help from people in the Greater Launceston area, towns in the Southern Midlands, the northern suburbs of Hobart, Gardners Bay and Rokeby.
"In the North, SES assisted with snow on the roads, water inundation through roofs due to snow melt and some wind damage," SES assistant director Leon Smith said.
"The conditions proved challenging for responding crews, with snow and ice preventing crews from working at heights.
"Our volunteers in the south responded to incidents relating to roof damage and water inundation in homes from ground level and through ceilings. SES also assisted Tasmania Police with road closures and traffic control."
Mr Smith reminded Tasmanians that there were "proactive steps" they could take to protect themselves in severe weather conditions.
"These include clearing gutters of debris and tying down any loose items outside," he said.
"When there is a non-life-threatening flood or storm emergency, SES can be contacted to assist."
Visit the SES website for further preparation advice
UPDATE, 10.30AM: In a statement issued about 10.10am, Tasmania Police urged motorists to drive to the conditions on elevated roads, due to the potential for them to be affected by snow, ice, rain and damaging winds.
Police warned that motorists "should adhere to cautions regarding icy conditions".
The following roads are closed due to the weather:
ROADS OPEN ONLY TO FOUR-WHEEL DRIVE VEHICLES:
EARLIER: Damaging winds and heavy rainfall are forecast in parts of the state until early this afternoon, the Bureau of Meteorology says.
About 5am on Wednesday morning, the BOM issued a severe weather warning for people in Tasmania's North-East, East Coast, Midlands and parts of the South-East, Central North and Central Plateau forecast districts.
"A low pressure centre close to the East Coast of Tasmania is directing a strong south to southeasterly airstream over parts of the east of the state," the update from the bureau read. "The airstream tends more south to southwesterly during the day."
The damaging southerly winds, which will average 60-70 kilometres per hour, with peak gusts of 90-100 kilometres per hour, are expected to affect areas in the state's East, as well as in the lee of the Central Plateau.
Furthermore, gusts of about 110 kilometres are possible in places such as Swansea and Bicheno.
"Damaging winds are expected to contract to the East Coast of the state by around sunrise on Wednesday morning, then clear the East Coast around midday," the BOM said.
Meanwhile, heavy rain - that could lead to flash flooding - has been forecast in the Midlands district until later this morning. The bureau said six-hour rainfalls of 50 millimetres had been recorded at Ross and Tunnack: "Rainfall in the Midlands district is expected to ease during the morning, and develop about the East Coast where 50-70 millimetres is expected, with rainfall in excess of 90 millimetres possible about high ground in the North-East."
Locations that could be affected include Campbell Town, Scottsdale, St Helens, Swansea, Fingal and Orford.
People are advised to supervise children closely, check that family and neighbours are aware of weather warnings, manage any pets and livestock and secure outdoor items like furniture and play equipment.
For emergency assistance, contact the State Emergency Service on 132 500.
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