The extreme weather could be the result of freezing Arctic winds blowing across the country.
Today, The Met Office issued a yellow weather warning for Yorkshire. The warning is due to take effect from tomorrow (Wednesday) and could last until the weekend.
The warning says: “Further showers of snow, sleet and hail will continue across parts of the UK. 2 to 4 cm of snow may affect some areas, while high ground may see locally 5 to 10 cm.
“Disruption to transport networks seems likely either due to snow or ice.
Additionally, strong winds and large waves will affect some eastern coastal areas.
“A cold northerly airstream will keep the risk of wintry weather going through Friday. Some inland areas, sheltered from the northerly wind, seem likely to escape most of the showers.”
With the cold air originating over Arctic Canada, Met Office meteorologist Emma Sharples warned: “We could get some blizzard-type conditions, especially at height.”
Talking about “thundersnow”, where the rain associated with a thunderstorm falls as snow, she said:
“It is possible, all that really needs is for thunder to happen at the same time as the snow.
“So where you get very active or vigorous showers - which is what we are going to see... then we could well get some thunder as well. It is definitely possible.”
Ms Sharples said the snow at lower levels will come in the form of showers and is unlikely to build up too much, unless there is “shower after shower coming over the same location”.
But she warned: “Even a centimetre of snow in this country can obviously cause some disruption,” adding that there could be “some showers inland, but they are likely to be short-lived”.
The Met Office said: “Lightning may accompany the heaviest showers, with potential disruption to power supplies as a consequence.”
On Wednesday and Thursday, wind gusts of up to 55mph are expected in exposed coastal areas and on hills.
Overnight frosts are also set to develop in most places, with severe frost likely where there is snow on the ground in the north.
In terms of temperatures, Ms Sharples said: “We are looking at low single figures, 2C to 5C by day, and then overnight it will vary across the country.
“But where there is snow lying it could be heading towards double minus figures, minus 8c or minus 10C, especially in towns and cities, and probably in the north of England and Scotland.”
Rod Dennis, of the RAC, said drivers should be prepared for “tricky driving conditions and significantly extended journey times”.
“Even a small amount of snowfall has the potential to cause major disruption for motorists. The fact that drivers in some parts of the country will be faced with strong winds, snow showers and icy stretches increases the chances of problems on the road enormously.”
He urged drivers to plan their trips carefully and “consider rearranging any non-essential journeys in the parts of the country most likely to be affected by the bad weather”, as well as checking tyre tread and pressure, windscreen wipers and screen wash levels.
“When out on snowy roads, always have dipped headlights on and proceed carefully and cautiously.
Drive with a very light right foot, and keep your revs down by changing to as high a gear as possible.
“Try to avoid braking and turning at the same time. When approaching a bend in the road, reduce your speed first and then begin to turn. Above all, avoid the temptation to brake sharply as that will make you lose control.”