The Ministry of Defence says it has three battalions on standby to respond to weather-related emergencies.
The Met Office has now issued an amber weather warning for snow in West Yorkshire for Tuesday and is predicting up to 20cm (7in) of snow in some parts of by the end of Wednesday.
The worst of the wintry weather is expected to arrive in the early hours of Tuesday morning.
The wind chill in the UK, which could see parts of the country drop to temperatures as cold as -15C (23F), is on par with forecasts for parts of northern Norway and Iceland.
Heavy #Snow plus strong winds will give some very difficult travel conditions across parts of northern England during Tuesday morning. 5 to 10 cm of snow is likely so take extra care when out and about ❄️#weatheraware pic.twitter.com/MNUUFprGbx— Met Office (@metoffice) February 26, 2018
Public Health England has urged people to check on elderly or vulnerable neighbours during the cold spell.
Members of the public have also been asked to look out for the homeless and report anyone sleeping rough in the freezing conditions to their local council.
Amber warnings of snow have been issued for northern, central and south-eastern England on Tuesday, and eastern Scotland on Wednesday.
The Met Office said rural communities could become cut off, with power outages and disruption to mobile phone services likely.
A less severe yellow warning for snow is in place from Monday to Wednesday.
Sky News weather presenter Isobel Lang said: "Tonight will see a penetrating frost with snow showers becoming heavier especially across southeast England and the Thames Estuary along with southern Scotland and northern England.
"Tuesday and Wednesday will bring further showers, and some more persistent snow belts which will pushouthwestwards across the country through the day.
For the latest weather forecast click here.
For the latest travel information for West Yorkshire click here.
For Bradford, Calderdale and Kirklees school closures click here.