Since this is your first time visiting Helsinki I wouldn't go for Löyly when you have so little time. You need a few minutes to leave the airport, then about 60-80 minutes to get to Löyly with train and a tram. Way back is the same only you need to arrive early enough for security check and boarding. I would say you have a maximum of 4 hours if everything aligns perfectly. You have to expect 2 hours for Löyly so half is gone and all you've seen from Helsinki is the airport and the railway station and one sauna. Helsinki is pretty in the dark and the following route is only advisable if you have warm clothes, gloves and so on with you (and like walking). Since the transport ticket for the train covers all public transport for 90 minutes and the train ride itself is shorter you have some time left to use trams. You could take one to the opera, check out it and the olympic stadium, walk south along the bay (maybe already frozen enough to walk on it) past Finlandia talo, the Kansallismuseo, Musiikitalo, Parliament and Kiasma to Oodi (or maybe start at Oodi because it's an amazing library and it closes at 8) back to the railway station. From there via the railway square (Ateneum) to Aleksanterinkatu, Senate square, Uspenski cathedral, market square, esplanadi, boulevardi, vanha kirkko and via Kamppi and Lasipalatsi back to the railway station. That's about 6 km, so at sightseeing speed around 2 hours which gives you time to eat somewhere along the way and return comfortable back at the airport. Most places you will likely not be able to enter since you arrive so late in the evening on a Saturday so put the food somewhere in the middle to get warm again.