The Met Office also warned about the dangers of damaged trees and other structures and said travel delays on roads, as well as rail and air travel, are likely.
Temperatures could get down to as low as -2C or -3C in Edinburgh and Glasgow Monday night into Tuesday, with the wind chill making it feel considerably colder.
Official weather warnings are in place for persistent snow and a risk of ice, with some areas likely to see falls up to 25cm during Sunday.
Sky News meteorologist Chris England said it would turn "much colder" over the next few days, with a "raw wind from the Baltic bringing widespread snow showers".
He said: "We don't expect anything like the same impact as a result of it, although there will be some snow about".
Forecasters said the snow, feeding in from the North Sea, was starting to spread westwards across to the Midlands and parts of Wales on Saturday morning.
Snow showers continuing to ease overnight and will become more isolated.
FREEZING weather, snow and icy conditions have returned across the county in the last 24 hours, and forecasters are warning of more to come.
The Met Office warnings for snow and ice begin at 6pm on Friday for eastern Scotland and England, and run into all of Saturday, where nearly the entire country is included.
Heavier snow and strong winds are expected, with some areas set to receive up to 10cm (3.9in) of snow and 30-to-40mph gusts of winds - causing travel disruption and extended journey times.
Just when we thought spring had finally arrived, the Beast From The East made a comeback at the weekend.
He added: "It's worth remembering that cold temperatures - indoors and outdoors, can affect health, particularly in young children, older people and those with heart and lung conditions".
Chance of showers in east. Snow will thaw in most places except across highest ground where temperatures remain below freezing.