Swedish weather agency SMHI issued an orange alert for central Sweden – covering the area around Stockholm, Uppsala, Gävle and Örebro – warning of snow and strong winds.
It said 15-25 centimetres of snow could fall, or 30 centimetres in some areas.
An orange warning is the second-most serious on a three-step scale, and means that there is a large risk that roads, as well as buses, train and flights, will be affected.
At least six traffic accidents were reported in the Stockholm region between 6 and 7am, according to the TT newswire, and several trains and buses were delayed or cancelled. In Örebro, all public transport was cancelled in the city, reported public radio broadcaster P4 Örebro.
Several other parts of Sweden also reported weather issues on Monday.
In the Östergötland region, a car held up traffic on the motorway after it went off the road near Melby, reported regional newspaper Corren.
In southern region Skåne, strong winds caused transport operators to cancel several trains, and tall vehicles were advised to avoid the Öresund Bridge to Denmark.