A severe weather warning indicated more snow would start falling this afternoon and that up to 15cm could fall by Sunday.
The forecast said winds would pick up today, leaving it feeling as cold at -7°C.
There could be disruption to travel and surfaces could become icy.
Wakefield Council said gritting teams were on standby.
And they warned people not to sledge at Sandal Castle, due to the moat being full of water under its frozen surface.
Council leader, Coun Peter Box, said: “We are as well prepared as we’ve ever been for bad weather and we are monitoring weather forecasts to make sure we respond quickly. Gritting crews are on 24 hour stand by for priority routes. We are very grateful to all our volunteer snow wardens who are ready to help in local neighbourhoods if there is heavy snow and would remind everyone to be public spirited and look out for their neighbourhoods and family members.
“Ultimately though we cannot compete with the force of nature and if we get a severe snowfall we will do our best to keep roads open and make sure vulnerable people get what they need, but some disruption is inevitable and people need to be extra careful and not head out unless absolutely necessary.”
The Highways Agency urged motorists to check forecasts before travelling.
And train operator East Coast has warned passengers to check for disruptions before travelling.
The company, which has worked closely with Network Rail to keep stations clear, has also advised people to travel before 6pm, when the worse of the snow is forecast.
It has lifted ticket restrictions for its London King’s Cross services for all journeys departing or bound for the capital.
For more details visit www.eastcoast.co.uk