Weather warnings have been issued by forecasters with more snow expected to fall across large parts of the country.
The Met Office said strong winds could lead to blizzard-like conditions, particularly over higher areas in the north, with the public told to prepare for possible disruption to travel.
Amber "be prepared" alerts were issued for parts of the Highlands, Grampian, Strathclyde, Central, Tayside, Fife, south-west Scotland and Lothian and Borders for Friday morning into the early hours of Saturday.
Forecasters said four to eight centimetres is likely to fall quite widely in the amber warning areas, with a low risk of more than 10cm locally - even on lower ground. Further north, 10 to 20 cm could fall on higher ground.
Transport minister Keith Brown said the weather could result in a "testing" journey for some people but said the Multi-Agency Response Team (MART) will monitor conditions and provide help across the network.
The same warning will also extend into northern England and the Midlands, meaning cross-border road, rail and air links could be impacted.
Mr Brown said: "According to the latest Met Office forecast, a combination of freezing temperatures, hard-packed ice and fresh snow will mean a testing journey for some people tomorrow. I would urge the public to take on board police advice about driving to the conditions, planning ahead and taking notice of travel updates.
"Despite the high level of service and winter treatments provided, sudden weather changes can occur, and stopping distances increase tenfold when driving in snow and ice."
Assistant Chief Constable Allan Moffat, from the Association of Chief Police Officers in Scotland, said: "We would urge people to be aware of the threat of disruption and to check with radio and TV bulletins and online before making their journey.
"It is also important that the advice and warnings given to those wishing to travel in the areas affected are heeded as the conditions may be hazardous."