A spell of snow, persistent and possibly heavy, is expected during Wednesday night and early Thursday.
Travel delays are likely on roads with a risk that some vehicles and passengers could become stranded.
Some rural communities could become cut off. Power cuts may occur and other services, such as mobile phone, may be affected.
Delays or cancellations are likely to rail and air travel and school closures are possible.
A spokesman for the Met Office said: “A deepening area of low pressure is expected to track east across the UK during Wednesday night and early Thursday. A spell of persistent and heavy snow is expected to develop. 3-8 cm of fresh snow is likely to accumulate widely with up to 20 cm over high ground.”
This new Amber Warning will bring further snow to Cumbria and southern Scotland as was experienced late on Tuesday/early Wednesday, and which caused widespread travel chaos on the A74(M) and other roads in Dumfries and Galloway.
Superintendent Graeme Galloway from Police Scotland said: “Even with a full scale response with snow ploughs and gritters on primary routes throughout the region, the main A74(M) did come to a standstill and many miles of standing traffic were delayed on both the north and southbound carriageways.
“A number of other primary routes were also blocked by snow.
“Resources from the Moffat Mountain Rescue Team were deployed throughout the night to check on the welfare of those caught up in the standing traffic, however no serious incidents were reported.
“The issue of another Amber Warning for our area means that once again resources are likely to be at full stretch tonight trying to keep our roads open. An Amber Warning carries the advice of Be Prepared, and as such I would ask members of the travelling public to first of all ask themselves the question about the necessity of their journey, and if they do need to travel, then please be prepared.
“Carry an emergency kit, which should include, a torch and spare batteries, warm clothing and blankets, a pair of boots, first aid kit, food and a warm drink, and make sure that mobile phones are fully charged.
“I would also urge people travelling through our region to check ahead with weather forecasts and also to check ahead if their proposed travel route is clear. The Met Office weather warning system is designed to alert the public to forthcoming weather events and I would ask that the public pay heed to these warnings, so they are not caught out.”
Dr Thomas Waite of the Extreme Events team said: “Cold weather like this is part of winter – but just because we’re used to it doesn’t mean we shouldn’t take steps to protect ourselves from falling ill. Every winter thousands of people die from illnesses linked to exposure to the cold when indoor and outside – that’s why it’s so important we all look out for each other.
“If you can, check on family, friends and neighbours who are older, have young children or who have heart and lung conditions all these groups are particularly vulnerable to cold.
“Keep a close eye on weather forecasts so you’re up to date with what’s happening in your area, keep homes heated to at least 18C and remember wearing several thin layers can be more effective than fewer thicker ones.”