Snow as low as 100 metres and a strong south-westerly will make for a cold start to the first working week of spring.
Bureau of Meteorology forecaster Tristan Oakley said the combination of wind speed and temperature will make for a cold few days.
Tasmania Police has issued several road warnings for Tuesday, including a warning for northern motorists to only access Poatina Village to Lake Secondary Road; Lake Secondary Road to Miena and roads to Golden Valley by four-wheel-drive.
Police said anyone travelling on Anthony Main Road, Belvoir Road and Murchison Highway should proceed with caution.
The Bass Highway at Deloraine, near the Meander Valley Bridge area, is open but a black ice warning has been issued.
Police said the Lyell Highway from the Derwent Bridge to Queenstown is restricted to four-wheel-drives and motorists should proceed with caution.
Cradle Mountain Road, Lake Dove Road and the road from Rangers Station to Lake Dove Road have all been closed.
The Ridgley Highway at Highclere, abouht four kilometres west past the Highclere show, has also been closed.
To stay up-to-date with road closures, visit Tasmania Police’s community alerts page.