Temperatures in the region are due to drop to -5 degrees and lower in rural spots, with freezing fog also forecast.
Drivers are being warned to watch for ice, particularly on untreated roads, and pedestrians are warned that paths could be extremely slippery.
Weather forecasters say the Arctic blast from the north will mean temperatures will struggle to get above freezing through the rest of the week and will drop overnight to at least -5 on Wednesday and Thursday because of clear skies.
Dozens of community venues have been opened up as warm spaces in initiatives by both Shropshire Council and Telford & Wrekin Council.
While many have reported only a few people using the sites, the organisers say the current cold snap is an ideal time to go along and see what is on offer - from free hot drinks and soup to social activities.
The leader of Telford & Wrekin Council, Shaun Davies, said the weather brought with it anxiety for those in fuel and food poverty.
"There are some stunning frosty landscapes and none more so than the Wrekin, it really looks a picture," Councillor Davies said.
"The cold snap, however, is not so welcoming for people worried about rising energy bills. That's why we’ve worked with partners to open warm and welcoming spaces around the borough. Anyone can visit to socialise and take part in activities."
People are being asked to check on older and vulnerable neighbours to ensure they are coping with plummeting temperatures.
Councillor Davies also issued a rallying cry for volunteers to come forward to act as snow wardens.
"We need community-spirited people to volunteer to grit icy footpaths and clear snow," he said.
"The national yellow warnings for ice continue into next week and these conditions can be treacherous. If you would like to join our army of volunteer snow wardens and help vulnerable residents, please get in touch. It's a great way to meet your neighbours."
One of the warm space sites is that run at the Salvation Army's Shrewsbury headquarters in Salter's Lane, Longden Coleham.
A spokesperson at the centre said: "We haven't had many people call in but we are open and very welcoming to everyone."
She said that the Salvation Army shop in the town centre had also dropped the prices of warm clothes.
"There is a special rail of clothing at reduced prices for anyone who just can't get warm at the moment," she said.
The cold snap looks like easing slightly on Sunday but the change could bring with it sleet and even snow on higher ground.