Police have warned impatient motorists to not "venture off" main roads after several cars become stuck in the heavy snow.
The country has already seen several travel disruptions as the Met Office declared a rare red weather warning on Friday.
Storm Arwen left a trail of devastation where gusts took up to nearly 100 mph on Friday.
The strong winds led to widespread travel chaos on Friday and Saturday, with trains cancelled, roads blocked and cars damaged by fallen trees and debris.
Many areas across the country also reported transport being disrupted, power cuts and damages to buildings - while heavy snow saw lorries get stuck and ploughs being used in a number of areas.
As well as blistering winds, temperatures are rapidly dropping, with reports of -1C forecasts in Manchester and Newcastle.
Emergency services have been assisting authorities in the cleanup operation throughout Saturday and Sunday while another alert for more snow and ice has been issued.
On Sunday morning, Durham Police took to Twitter to urge motorists to not venture off the main roads unnecessarily.
The post said: "Our car can get to most places and we'll go wherever we can to help!
"Some of the minor roads remain poor in Teesdale along with cables and trees down, yet some motorists are ignoring the road closures."
The road closures come just as Storm Arwen wreaks havoc across much of the UK, having already claimed three lives.
Police Scotland said a 35-year-old man died when his pick-up truck was struck by a falling tree in Aberdeenshire at about 5.45pm on Friday.
Cumbria Police said a man from Lancaster died in Ambleside after a tree fell on him.
In Northern Ireland, a man was killed when his car was hit by a falling tree in County Antrim.
Many others across the UK have been left devastated by the storm, with The Mirror reporting many households in the North West have been left without power for two nights as engineers scramble to bring electricity back.
Snow is expected to continue to fall in most parts of the region and police are urging motorists to watch out for road signs while driving.
As well as snow, motorists are told there is a risk of "icy stretches", with snow showers becoming more extensive over parts of Scotland and the north-west of England early on Sunday.
The spokesperson added: "Please don't venture off the main roads unnecessarily and watch out for signs!"
The Met Office has expanded a warning for snow and ice for Scotland and the north of England with roads possibly being treacherous.
