....simple answer is....
yes, they do !!!
so I can stop my post here :-) ...joking, of course.
I am wondering how to describe it, but my general feeling is that motion is part of Swedish culture, it is some kind of awareness that you should do it for your own good, for your health and happiness.
It is so easy to discuss with them about sport, everyone has something to add, most of them are very active, in worst case it is golf :-) I discussed with many who finished at least once (but usually many times) half marathons or even marathons. It seems that fact that you can run 10 km is not very impressive here :-). I met persons who finished full Iron Man Competition or they are preparing for it.
Every time when I go running I meet others runners and bikers or power-walkers or roller skiers, seriously every time!!! even when it was -4 C and full of snow I met runners. During my last Sunday jogging I counted around 10 other runners and at least the same number of bikers. It's impressive because it isn't Stockholm or Malmo- it is really small city, similar to which I live in Poland, where sometimes I met other runner...sometimes.
And is not like that everyone is training so hard every day, but many take light motion activities, here power-walk is very popular - I met many people in sport cloths just marching in a little faster pace - it's not very aggravating but it is very good for your health and comfort.
Sport is really part of they life, so I fell that I will write about it many more times :-)