The Met Office forecasts snow showers will continue during Monday night and Tuesday, with some large build-ups in parts of central Scotland.
Up to 10cm is expected to lie fairly widely on Tuesday while it could reach 25cm in one or two spots.
Transport Scotland has warned of long delays as well as cancellations to bus and rail services.
Transport Secretary Michael Matheson said: "We're being warned that parts of Scotland are expected to face another period of challenging weather, with the Met Office issuing an amber snow warning for Tuesday.
"The current Covid-19 restrictions mean you should only be leaving your home for an essential purpose, so please consider if your journey is absolutely necessary before setting off.
"The forecast conditions will likely cause difficult driving conditions and disruption to the wider transport network.
"If you do have to make an essential journey, then the advice remains the same as it has throughout this winter.
"There may be disruption on other modes of transport, so you should check with your operators before setting off."
The amber warning is in place between 3am and 9pm on Tuesday.
A further yellow alert for snow, which covers the central belt and eastern Scotland, is already in force and is expected to stay until at least Wednesday evening.
Areas such as Edinburgh and Glasgow have already faced a loss of electricity supplies amid the wintry weather.
Roads over higher routes are particularly expected to be affected by the snow and some rural communities might be cut off.
The Met Office predicts temperatures could fall to around minus 12C (10.4F) around Grampian into Tuesday morning, while later in the week it could fall as low as minus 15C (5F).
Luke Miall, forecaster, said: "Later in the week we start to see the strong easterly winds come down a little.
"When you have lighter winds it's better for getting accumulations of snow.
"It's probably going to be Wednesday night into Thursday.
"Certainly somewhere like Braemar, that could be one of the coldest, but it's going to be cold everywhere.
"We barely got above freezing across Scotland today."
Braemar has already seen almost 70cm of snow on Monday.