It IS special experiencing the snowy countryside with a pack of dogs. Several places in the area offer tours, not least the Ice Hotel if you stay there (they can even pick you up from Kiruna airport with dogs). Otherwise, ask the tourist office for an updated list.
Equipment: Most will lend you warm overalls.
I think there is a place where you can go skiing or snowboarding, but I'm not sure where it is. We decided to do other activities instead of winter sports. You can probably ask the locals where to go for winter sports.