Vilte Lahti is the place for winter sports and especially well known for ski jumping. Winter games are hosted all the time.
Well Helsinki is not so big, but it is worth to take some ferries around like they have zoo I one island, there is all fort as well, and some nice nature walks around Helsinki and Espoo, as well Vantaa city is near by worth of visit. And I would for sure suggest Porvoo is it very cute and old one.
Even in winter you can have some great hikes around.