Drivers are being urged to take extra care, as sub-zero temperatures stretched into the Christmas weekend.
The Met Office warning came as it said the weather had led to widespread ice on roads across Scotland.
Two police officers were taken to hospital after they were hit by a car while dealing with a road crash in icy conditions on the A77 near Kilmarnock.
Alex Salmond thanked emergency staff and other workers for keeping the country running over Christmas.
The government's resilience committee is reviewing the latest information on weather-related problems.
The Met Office said rain and sleet showers had caused ice to form on roads across the Highlands and central Scotland.
Northern Constabulary said all Highland trunk roads were open, but the force warned the freezing temperatures overnight meant a "significant risk" of black ice.
In the first minister's Christmas message, Mr Salmond paid tribute to all those who have helped keep Scotland going during the "extraordinary" winter weather.
"In these extraordinary circumstances, I want to break with tradition to pay a personal tribute to those who keep Scotland moving, working and smiling," he said.
"The white-out began in late November and has more or less continued since then, making this month the coldest since records began in 1910.
"Coping with the weather has been one of Scotland's toughest challenges of recent times."
The male and female police officers were taken to Crosshouse Hospital in Kilmarnock.
The woman is believed to have had a broken arm and ankle, and her colleague received minor injuries.
It is not known if ice contributed to the collision, and a Strathclyde Police spokesman said: "Inquiries are ongoing in respect of this."
On the railways, ScotRail urged train passengers to check services before travelling in the days ahead. It said it was constantly reviewing timetables and, where possible, it would run normal services.
There will be no rail services on Christmas Day and a limited Strathclyde service on Boxing Day. Latest updates will appear on the journey check website.
Steve Montgomery, managing director of ScotRail, told BBC Scotland work was carrying on to keep trains free of ice and snow.
He said: "Although it's not been snowing in the central belt, we've still seen quite significant snow in the Aberdeen and Inverness areas and trains are picking up a lot of snow, so we've still got to bring the trains back into the central belt and de-ice them.
"That's making a lot of work for over the weekend and we'll hopefully get most units sorted out for next Monday."