A yellow "be aware" weather warning is in place for Strathclyde, the Met Office said.
The warning continues: "Icy stretches are likely to form on untreated surfaces across Scotland and northern England during early Wednesday morning, with upland areas most prone in the early period following snow and partial thaw.
"Further wintry showers in the overnight period are likely to increase the ice risk by dawn on Wednesday.
"The public should take extra care and be aware of the risk of ice on untreated surfaces."
The warning will remain in place until late into this afternoon and it is expected to remain cold and mostly dry with temperatures barely above freezing across Glasgow for the day. Some sleet is possible tomorrow, which will begin with a widespread frost, ahead of a cloudier but still cold weekend.
The winds which prompted chaos with driving snow across the west of Scotland on Tuesday are expected to ease, meaning less chance of blizzard conditions.
The Met Office say the weekend is likely to see spells of rain and sleet although any remaining rain or snow will clear away through Monday.
Most areas will remain dry, bright and cold next week with overnight frosts and an ongoing risk of icy stretches.
More snow could be possible on higher ground.