The Met Office has issued a fresh weather warning for Dundee, Tayside and Fife and says temperatures are to plunge even further.
The yellow warning for snow and ice, valid until 11am, covers the whole region.
It says: “Further snow showers are expected into Wednesday morning, these more frequent across northwest parts of Scotland and Northern Ireland.
“Expect 1-3 cm of fresh snow even down to very low levels in places, but locally around 5 cm across the Northern Highlands.
“Ice is likely on some untreated surfaces.”
The warning adds that longer journey times are expected on some roads, and that injuries are possible from slips and falls on icy surfaces.
Britain itself faces “very significant snowfall” this week, with temperatures expected to drop to at least minus 10 degrees Celsius across the country.
A weather system forecast on Thursday could break this winter’s current record low of minus 10.8 degrees and bring up to 10cm of snow to parts of southern England.
Journeys on the roads could take “a lot” longer and should ideally be avoided if possible, said Met Office meteorologist Alex Burkill.
Current yellow weather warnings might also be upped to amber, and vulnerable people are warned to take extra precautions.
The weather front on Thursday will follow a band of snow, rain and sleet across the country on Tuesday night.
Mr Burkill said: “Looking further ahead, it’s what happens on Thursday that has the potential to be more disruptive.
“It does have the potential to bring some very significant snow. We have already got a warning out in force for it.
“It’s currently just a yellow warning, but it’s not out of the question that will be ramped up nearer the time.
“It’s looking like it will be a spell of persistent snow.”
The year’s record low, recorded in Braemar, Aberdeenshire, on January 18 is also likely to be beaten.
Benton, in Oxfordshire, and Santon Downham, Suffolk, are among parts of England which could be coldest.
“I think Scotland will probably be the coldest place but it’s not out of the question we got into negative double figures in parts of England,” Mr Burkill said.
Thursday will start off “very cold” as the weather system pushes eastwards from the south west.
Areas of higher ground could get up to 10cm of snow.
“It’s worth bearing in mind there will be some disruption, particularly to travel. If you’re heading out on the roads, be aware you’re journey will take a lot longer than normal,” Mr Burkill added.
“There’s an ice risk which is going to cause some problems so even if there is not snow it could be icy on the roads and pavement which people need to be aware of.”
Official Met Office figures for snowfall on Tuesday showed the worst-hit areas were Tulloch Bridge, Inverness-shire, with 11cm, and Spadeadam, Cumbria, with 10cm.
Councils have prepared for heavy snowfall, with more than 1.4 million tonnes of salt stockpiled, the Local Government Association said.
Public Health England has also warned at-risk people, including the elderly, to take precautions.
Dr Emer O’Connell, a public health consultant, said: “If you can, check on family, friends and neighbours who are older, have heart and lung conditions or young children as all these groups are particularly vulnerable to the effects of cold.”