A yellow weather warning for snow and ice from the Met Office is in place throughout Tuesday across the Highlands, Moray, Aberdeenshire and parts of Perth and Angus.
This is due to lift at 9am on Wednesday.
There is also a yellow wind warning in place from 10am on Tuesday until midnight for the northern and western isles, the north Highlands and the north east, with gusts expected to reach up to 80 mph.
A third warning has been issued coming into force on Friday.
A Met Office spokesperson said: “Showers, accompanied by strong winds, will become increasingly frequent and wintry through Tuesday at all levels, before dying away Wednesday morning.
"Below 100m, accumulations are most likely to be temporary and slushy. Above 200m two to five cm is likely in places with 10-15 cm possible on higher routes.
“Icy stretches are also expected in association with these showers, particularly where they fall as sleet to low levels.
"In combination with winds gusting 50 to 60 mph at times, temporary blizzard conditions and some drifting of snow on higher level routes is likely.”
Scots have been warned to expect difficult driving conditions, particularly on higher routes, and some disruption to public transport.
Major routes above 200m which could be affected include sections of the A96 around Huntly and Keith, the A95 between Aviemore and Craigellachie, the A9 between Dalwhinnie and near Inverness and the A97 west of Invergarry.
Traffic Scotland said on Tuesday morning that heavy snowfall this morning was impacting routes including the A9, A87, A82 and A90.
Urquhart Castle in Drumnadrochit, Inverness, has also been impacted by the bad weather, sharing an announcement on Tuesday morning saying it would be closed for the rest of the day.
Aviemore saw five centimetres of snow on Monday, which would have been added to overnight, forecaster Simon Partridge said, suggesting that this might be “good news” for the Cairngorms town’s ski resorts.
He added: “It’s basically what we should have for this time in January; it’s just that we’ve been so mild for so long that it’s suddenly a bit of a shock to the system.”
Those travelling should take extra precautions as there may be some untreated icy patches on roads, pavements and cycle paths.
Another yellow snow and ice weather warning for later in the week was issued on Tuesday morning from the Met Office.
It will come into force at midnight on Friday and lift at 10am, covering the Highlands, Glasgow, Dumfries, Galloway, Lothian and the Borders.
A Statement from the Met Office said: “Frequent wintry showers arriving from the west overnight Thursday into Friday are likely to lead to a fresh covering of snow for areas above 200m.
"Falling snow below this level may cause some temporary slushy accumulations which then may freeze and cause dangerous, icy patches where skies remain clear for long enough.
"These showers will turn increasingly to rain and sleet at lower levels through Friday morning, before steadily easing from the west through the afternoon ahead of an area of rain and milder conditions.”