"We have issued Class 2 warnings and the most powerful winds are expected in the southern peaks of Norrland. There's a risk of 25 or 30 metres per second. That's almost hurricane strength," said Alexandra Ohlsson of the Swedish Meteorological and Hydrological Institute, SMHI, to news agency TT.
According to the forecasters, regions of the counties Jämtland and Västernorrland look to be particularly in danger of being hit by the storm, although much of the country can expect strong winds.
During the afternoon on Sunday the Swedish Transport Administration (Trafikverket), announced that all rail traffic to and from Norrland would be halted from 8pm onwards in anticipation of the storm approaching from the west.
"The reason is that we are worried trains will be left standing following fallen down cables and other obstacles," said Peter Behrman of the agency to TT.
SMHI had already issued a Class 1 warning on December 23d and there were widespread problems on the roads throughout Christmas Eve as the weather progressively got worse across Sweden.
With Dagmar believed to be one of the most powerful storms of the past 30 years, Norway has been most seriously affected so far.
The Norwegian coast seems worst affected, with a Hurtig Ruten cruise liner having to postpone its trip between Bergen and Tromsø on Christmas Eve.
Parts of Iceland have also been hit by the gales.
A Class 2 warning is classified as weather which could pose a danger to the public, cause major damage to property and major disruptions in essential services.
People in Sweden intending to go out or travel have been advised to find out the latest information from the radio or on the internet before setting out, especially later on in the day.
There were already numerous reports of accidents on the roads on Christmas Eve and conditions in many parts could get even worse.
This is in marked contrast to the mild weather in the Stockholm area, where residents in Södermalm, in the southern part of the capital, reported seeing wild strawberries growing in the unseasonably warm conditions for the season.
Despite being disruptive to people planning to be out and about over the Christmas weekend, the storm is expected to blow through quickly as it makes its way further east over Finland.
Conditions should be more stable by Boxing Day on December 26th, according to forecasters.