The Met Office has extended yellow weather alerts for snow until Friday evening, with further falls of the white powder and freezing temperatures expected to hit most areas over the next few days.
Strong winds could exacerbate the conditions, causing blizzards and snow drifts and making travel hazardous.
As much as 40cm of snow could land on high ground, including the Southern Uplands, parts of the Central Belt and the southern Highlands. Even low-lying areas could get up to 10cm.
Temperatures could drop to -10C on higher ground where snow has fallen in what would be the coldest temperature so far this year.
People are being advised the heavy snow could cause “significant disruption”, potentially stranding homes in remote areas and causing long delays and cancellations for road, rail and air journeys.
Power and water supplies, telephone lines and mobile phone coverage could also be affected.
The Met Office has said snow could develop quite widely across the warning area on Thursday and Friday as a potentially quite deep area of low pressure moves across the UK.
Parts of Northern Ireland, north Wales and northern England are expected to see the worst of the conditions on Thursday, with parts of Scotland and northern England then seeing the heaviest snow on Friday.
“In addition,” the Met Office warned, “there is potential for strong winds, which may lead to blizzard conditions and drifting of lying snow.”