The Met Office has issued two yellow weather warnings for Monday 26 December, with snow and ice alerts in place across large parts of Scotland.
Ice warnings are also in place for most of Northern Ireland.
Traffic is set to build around shopping centres, as bargain hunters are forced onto the roads instead of railways.
The AA expects 15.2 million cars on the roads throughout Monday, but says many will be making short trips that are likely be spread out across the day.
A spokesman said: "Traffic is likely to build around shopping centres as lots of people seek a bargain in the sales, meanwhile football fans will travel to see their teams."
Temperatures are expected to hit -4C (24.8F) in the Scottish Highlands and about 4C in Northern Ireland.
The Met Office's weather warnings for Boxing Day include yellow alerts for:
* Snow and ice for most of the Scottish Highlands, as well as some lowland areas until 18:00 on Boxing Day
* Ice to hit Belfast and Newry in Northern Ireland from 00:00 to 10:00 on Boxing Day
The Environment Agency has 42 active alerts for possible flooding in England.
Separately, 24 flood warnings - meaning flooding is likely - are in place for areas including River Severn in Gloucestershire, Tyne and Wear coast, and River Trent in Derbyshire.
Met Office meteorologist Rachel Ayers said blizzards could hit high ground.
She said: "Showers, which will be wintry in places, will continue across Scotland, Northern Ireland and far northern England, locally these could be heavy with hail or a thunderstorm possible.
"Any accumulating snow will be mainly over high ground where there is a risk of blizzards.
"Showers easing into the later part of the afternoon.
"Windy for all, with gales in places especially across the Northern Isles."
It will be milder further south - with Birmingham expected to see about 5C and London and Cardiff expected to be around 7C.
Network Rail has said railways across the UK will remain closed for a second day due to a walkout by employees who are members of the Rail, Maritime and Transport (RMT) union.
Merseyrail is due to run a half-hourly service across its network on Merseyside, with its website saying trains will run between approximately 09:00 to 18:30 and only stopping at selected stations.
ScotRail usually has a Boxing Day service in the Strathclyde area - but there will be no services there this year.
Northern operated a service between Liverpool Lime Street and St Helens Central on Boxing Day last year, but the company has said there will be no trains running on Monday.
There will also be no Southern services.
Trains do not usually run on Boxing Day, apart from some airport transfer services, such as the Stansted Express and Heathrow Express.
Instead, people can travel on Megabus or National Express bus services if they need public transport, as they run on Christmas Day and Boxing Day each year.
Meanwhile, people planning to jet off for a festive getaway will need to find other ways of getting to and from the UK's airports.
Airport transfers including the Heathrow Express and Stansted Express tend to be the most popular services on Boxing Day.
The RAC also highlighted two stretches of the M25 as likely hotspots for traffic - including from junction 7 to 16 clockwise, and from junction 4 to 1 anti-clockwise.