Winter Sports, Stockholm
From mid November to end of February, you can skate in Kungsträdgården in the city centre and it is open most days. There are also skating rinks elsewhere in the city when proper winter comes and some of the football grounds are watered and freeze, but then you have to know where to go (or check the official tourist site which might give you tips).
If you are a skilled skater, you might also enjoy a full day out on a Swedish lake or the archipelago in winter, but do bear in mind that you have to be sure of the ice quality (less frozen where ferries shuttle in the archipelago for instance) and have the safety equipment needed for that. Try www.friluftsframjandet.se and pop into their Stockholm section for further advice.
Equipment: There are skates to hire in Kungsträdgården if you haven't got your own (SEK 30 for adults in 2005)
If in Stockholm a snowy winter, buy yourself a cheap toboggan in a toy shop (or try a plastic bag) and head for Sofia on Söder. The Vita bergen park here sees adults race each other in the evening when the children are back at home...:-)))
At Sodermalm, I came across a ice skating arena where children were skating. It was in the middle of a square in front of the Södertorn
It is a small Skislope near Drottingholm in Ekerö. For times you don't want to drive very far up North, you can go there for the day.
Equipment: They rent out all the equiptment, accept for snowbords.