In Helsinki to see the northern lights is pretty rare. There might be quite often them, and if you see northern lights they come out pretty light. I've seen twice northern lights in Helsinki, and both times it felt magical. It truly is as amazing and I totally understand why Japanese people travel 9 000 km to see them. I can't even imagine how nice it must be to stand in some empty space in Lapland and watch northern lights. It could be meditative as well!
Best time to see northern lights is when the first frost comes (around September), or then when the winter is it's cold (January-February).
I was in the hill of Alppipuisto with my friends and suddenly we noticed the northern lights wiping over Pasila..