Forecasters said a band of rain and hill snow will push eastwards, while Scotland and Northern Ireland are expected to see strong winds with coastal gales.
There will be sunshine and some rain for the southern and western parts, although showers are forecast to be heavy with hail and thunder mixed in.
Temperatures will remain on the cold side, with around 5C or 6C the maximum for many and 10C expected in the south-east.
The higher temperatures didn't prevent people being hit by snow after flurries fell in London.
Met Office meteorologist Helen Roberts said the country could expect a continuation of sunshine combined with heavy, blustery showers today, with snow causing some "localised problems" in the north.
"Probably more of a risk than the snow, or more of a hazard, is going to be ice because temperatures will drop very quickly in clear slots," she warned.
Roberts said a low pressure system was dominating and prolonging the wintry conditions.
She added: "Its quite a deep low and it's not moving anywhere very quickly, it's just swirling around these showers across the country."
Little change in the conditions is expected for tomorrow, although the focus for most of the showers will be in the south-west of the UK.
The Met Office also confirmed last month was among the wettest March on record in the UK.
Provisional figures show the UK had an average 132.9mm of rainfall - the fifth wettest since data was collected in 1910. The all-time record for March is 150.3mm, which was set in 1981.
