The lowest temperature recorded overnight was minus 9.8C (14.4F) at Strathallan in Perthshire, the Met Office said.
The mercury dropped to minus 9C (15.8F) at Glasgow Airport and minus 8C (17.6F) at Edinburgh Airport.
Police warned motorists to drive carefully in the freezing conditions.
At 8am on Monday police tweeted: “Road traffic collision reports are coming in fast this morning ... 25 in the last hour alone.
“These sometimes cannot be avoided, but please remember that stopping distances can be up to 10 times longer in icy conditions.”
The cold snap is expected to ease slightly over the coming days.
Ian Robinson, of the Met Office, said: “We’ve started to see a pick-up in wind speed from the south and there should be a cloudy spell of weather coming.
“The very low minimums of the past few days are probably not going to be repeated.
“It may be down to minus 3C (26.6F) tonight but generally minimum temperatures will not be as low due to increasing wind and cloud.”