Cars were abandoned and roads shut in Stoke-on-Trent after up to 3in of snow fell. Rail services are also disrupted.
Authorities in Staffordshire and Gloucestershire urged people not to travel unless absolutely necessary.
A Met Office yellow warning of snow and ice for much of England and Wales and parts of Scotland remains in place until 10:00 GMT on Tuesday.
There were reports of delays, stranded motorists and abandoned cars on the A53 at Etruria and in Hanley, in Stoke on Trent, with more issues on the A34, in Stone, and on the A500.
Police in Lichfield said the Burntwood bypass, between the M6 Toll and Miners Way, had also been closed due to a crash.
They said officers across Staffordshire were dealing with "numerous snow-related incidents".
Delays were reported on rail services through Stoke-on-Trent from both Manchester Piccadilly and Birmingham New Street.
Stoke-on-Trent City Council said it would be gritting until about midnight on Monday and had sent snowploughs out to clear routes, with temperatures expected to be freezing again from 18:00.
It said it had only expected light flurries but in some places about 3in (7.6cm) of snow had stuck.
Heavy snowfall prompted Gloucestershire Police to warn members of the public to take care and to "only go out if it is essential to do so", with particular problems in the Forest of Dean and on the A417 around Birdlip.
Elsewhere, Dudley Zoo closed for the day and a football match between Kidderminster Harriers and AFC Telford United was called off. A number of roads in Worcestershire were shut.
As well as the snow, there are dozens of flood warnings in place in England.
Large swathes of London, the Midlands, the South, the South West plus the east of England and Wales have been warned more freezing weather could hit on Wednesday and Thursday.
The Met Office yellow warning suggests that up to 2in (5cm) of snow could fall across parts of southern Wales, and central and southern England. There is also a small chance of up to 6in (15cm) settling in a few places, most likely on high ground above 200 metres.
There is also a risk widespread ice could form on untreated surfaces as the rain and snow clears on Wednesday night.
A woman cleared a path in Burford, Oxfordshire, which could see more snow on Wednesday and Thursday