Forecasters predict freezing temperatures and strong westerly winds for the city, which could result in hazardous travel conditions for commuters.
The worst-hit areas are likely to be the high ground, where "significant" snowfall is expected throughout the day.
Yellow "be aware" warnings for snow and strong winds have been issued across the Glasgow area.
Met Office forecaster Peter Sloss warned residents to wrap up warm and take care on the roads. He said: "It is going to be a very windy day, with gale force westerly winds.
"The temperatures remain quite low during the day, so it will feel bitterly cold.
"The other issue will be showers, because it is so cold the showers will be sleet and snow.
"Higher ground will see significant amounts of snow."
Tomorrow, the snow should turn into rain in the city, with wintery showers confined to high ground.
The cold weather will continue into Wednesdaywhen it will be dry and quite sunny.