But falling temperatures and wind will give a more wintry feel from Wednesday onwards, according to a forecast from the Danish Meteorological Institute (DMI).
"Monday is a little bit special, because we currently have a warning out of heavy fog in large parts of Jutland and Funen, but that should be over during the course of the morning," DMI's meteorologist Lars Henriksen said.
"Apart from that, Monday will be a cloudy day. Particularly in the southeastern art of the country, where there will also be rainy spells," Henriksen added.
Temperatures on Monday will be between three and six degrees Celsius.
Tuesday is forecast to begin with rain across the south of the country and clearer weather taking over in the west as the day goes on. Temperatures will range from 3-6°C.
From mid-week until the weekend, dry but colder weather, dropping to seven degrees below zero at night, will see a return to the wintry feeling that has so far characterised March.
"We will return to a situation in which daytime temperatures will be between one and four degreed above zero with frost at night in many places," Henriksen said.
"Low nighttime temperatures will mainly be in the centre of the country, and there will be a good, fresh and sometimes hard easterly wind. So I'm afraid it will probably be a bit more wintry in the middle and at the end of the week," he said.
"That means it will be colder. And the wind will actually make it feel quite cold," the meteorologist added.