All flights at Arlanda were grounded for a time on Wednesday, but one runway was opened shortly after 10am to allow planes to take off.
However, no planes were yet being allowed to land.
"It's going to be like this at least until lunch. But we're going to have major problems all day," Klas Nilsson, spokesman for airport operator Swedavia, told the TT news agency.
Meanwhile, flights have been on schedule at Skavsta airport, located about 100 kilometres southwest of Stockholm.
The snowfall picked up pace during the night, confirmed the Swedish Meteorological and Hydrological Institute (SMHI).
"At 4am, the snowfall became more intense in Stockholm and in Sörmland and Uppland," said SMHI's Gustav Åström.
"We could see up to 20 centimetres more snow during the morning."
The storm caused a number of accidents across central Sweden, but none resulted in any serious injuries.
"The roads are in rough shape right now. If you don't need to go out, try to avoid doing so for the moment," Östergötland County police duty officer Lars-Göran Nilseryd told TT.
Sweden's postal service, Posten, also issued a statement that some customers in Stockholm, Uppland and Södermanland Counties may not receive any post on Wednesday due to the harsh weather.
Long-distance rail service was experiencing delays of up to an hour on some routes, with rail operator SJ warning that delays would likely worsen throughout the day.
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Buses in the Stockholm region are running but experiencing delays.
The metro, trams, and commuter trains are also running, but a number of commuter rail lines have been delayed by up to 45 minutes, according to the Stockholm Public Transport operator SL.