Snow is predicted for Sunday and forecasters say the city will shiver as temperatures plunge below zero during the next few days.
The snow and sleet is also set continue into next week.
Forecasters said there will be plenty of dry spells tomorrow, but predicted below-freezing temperatures and "persistent snow" by Sundat.
Cold air is expected to blow across the North Sea from Scandanavia tonight, increasing the risk of snow showers.
A spokesman for forecasters MeteoGroup, said: "Saturday is going to be very cold, but largely dry across Glasgow and the Strathclyde area.
"However on Sunday morning, a weather system will move in from the west and we will see sleet and snow pushing in with it.
"The sleet and snow showers will be fairly persistent, but fairly light.
"We are looking at between 20mm and 25mm of snow falling in the Glasgow area, throughout Sunday.
"Overnight temperatures in Glasgow on Saturday could reach -3°C and on Sunday, temperatures will struggle to reach above freezing."
Parts of the country were issued with "be prepared" warnings for sleet and snow.
The Met Office issued a yellow weather warning for snow showers to hit parts of the east and north of the country.
Fife, Dundee and Angus are expected to experience heavy snowfall on Saturday, as are parts of Aberdeenshire.
Forecasters warned motorists to brace themselves for wintry weather lasting into rush-hour on Monday morning.
A MeteoGroup spokesman added: "Looking forward to Monday morning, a further weather system will move in from the west.
"However, there is uncertainty about how much snow we will get."