Inari is one of the most reliable places in Europe to see the Northern Lights — far enough north to be inside the auroral oval, far enough from major light sources to keep the sky dark, with crisp clear winter conditions. The aurora can in theory appear from late August (once the sky is dark enough) through to mid-April; the deep-winter months (December to February) combine the longest nights with the highest activity.
You do not need a tour to see them — walk out to the lakeshore from the village on any clear evening between October and March. Several operators do offer aurora-hunting trips (snowmobile, husky-sled, or by minivan to remote spots) which add the experience of being out in the snow without needing to camp. Phone apps that track the solar Kp index are useful for picking the best nights.