Many tourists, especially the Japanese, come to Saariselkä to gawk at the aurora borealis. While they occur with a probability as high as 75% every night in season November to March or so, they are all too often obscured behind a bank of clouds so don't count on it.
But there's plenty of standard Lappish tourist fare to keep you occupied during the day as well, ranging from husky safaris and reindeer-pulled sleighs to snowmobile and snowshoe treks through the countryside.
For arctic scenery, climb or take the bus up Kaunispää to take in the view.