"Traffic seems to be moving slowly...The snow will likely continue to fall through to Sunday and then conditions could get tough, especially on smaller roads," Carin Berggren at Swedish Radio's traffic department said on Saturday afternoon.
There were a number of accidents Saturday, including one incident where two vehicles collided and a third skidded into a ditch between Vetlanda and Korsberga in southern Sweden. Four people were involved in the crash and one was admitted to hospital.
In another incident, four people - including two children - suffered mild injuries when two cars were involved in a frontal crash on the 558 county road between Köping and Munktorp in central Sweden.
Several single-car accidents were also reported in the towns of Timrå, Sundsvall, Uppsala and Västerås, according to news agency TT.
According to the Swedish Meteorological and Hydrological Institute (SMHI), up to three decimetres of snow was expected to fall Saturday in some locations.
"We have issued a Class-1 weather warning for several parts of the country," said SMHI meteorologist Lisa Frost.
A Class-1 warning means that weather conditions carry certain risks to the public and disruption of some societal functions.
On Saturday morning, several road derailments were also reported to Swedish Radio's traffic department, particularly in the Stockholm and Sörmland regions.
Carin Berggren advised motorists to be patient and prepared for difficult conditions, and to count on journeys taking longer than usual.