Travel disruption and power cuts are expected across the east of the Central Belt and southern Scotland, south from Edinburgh.
Transport Minister Humza Yousaf said work had already started to try to prepare for the wintry blast.
And there were early morning reports on Thursday of wintry weather already arriving.
In the north the A9 was passable only with care at the Slochd Summit due to swirling snow.
On the west coast there were ferry cancellations due to high wind.
The Forth Road Bridge was also clsoed to high sided vehicles.
In the Scottish Borders, all school transport has been cancelled.
The amber “be prepared” snow warning covers a large swathe of southern and central Scotland.
Accumulations of 10 to 15cm “are likely quite widely” with 20 to 30cm of snow possible on hills above 300m.
The warning lasts until 6pm tonight.
Storm Doris has also triggered an amber warning for 80mph winds across the northern Midlands in England and north Wales.
Separate warnings for gales in the far north and heavy rain in the far south of Scotland, and across the west coast on Saturday, have also been issued.
Transport minister Humza Yousaf said: “The Met Office is telling us that Storm Doris will bring a mixture of heavy snow, sleet and rain across central and southern areas and this will lead to poor driving conditions, especially around the Southern Uplands.”
The Scottish Government’s Transport Scotland agency said conditions were also likely to be “quite difficult” for gritters and snowploughs.
Superintendent Fraser Candlish of Police Scotland said: “With a substantial risk of travel disruption due to the weather, motorists should consider whether their journey is absolutely necessary.”
A Met Office spokesman said: “Accumulations of 10 to 15cm are likely quite widely, with 20 to 30cm falling on hills above 300 metres.
“This will lead to disruption to transport and perhaps power supplies.
“As Storm Doris moves eastwards across central parts of the UK on Thursday a spell of heavy snow is expected on its northern flank.
“There is some uncertainty over the track of Doris and therefore over the extent of snowfall, but confidence is now higher for disruptive snow to affect the amber area.”
For the yellow warning area, the spokesman said: “Snow accumulations of 5 to 10cm are expected on some hills with 2 to 5cm possible to lower levels to the north of the Central Lowlands.
“In addition, strong winds are expected to develop with gusts of 50 to 60 mph.
“This will result in drifting of the snow and blizzard conditions over high ground.
“Associated heavy rain at lower levels will be an additional hazard.
“The combination of snow, strong winds and heavy rain is likely to lead to disruption to transport networks and perhaps power supplies.”
A yellow warning for heavy rain has also been issued for the Highlands and west coast for Saturday. Up to 75mm is forecast between midnight and 9pm, which the Met Office could disrupt travel and cause flooding.