In December if it were me and my spouse, I would visit places she would find more interesting than me. In Helsinki I would want to take a ferry to Suomenlinna, visit the Stone church, visit the Espoo Temple, go to Porvoo old town, walk downtown and take the tram around and sightsee. I would go to the Itakeskus Swimming Hall, Allas Sea Pool or the Urheiluhallit Mäkelänrinne and swim and sauna.
In Estonia, but I would want to see the old town in Tallinn and the place where they do all the singing festivals and visit Tartu. Stay at least one night in Tallinn and then fly from Tallinn to Rovaniemi on Finnair for $131 (Cheaper than a $50 ferry back to Helsinki and flight from there as it stops in Helsinki anyway) and explore and do the touristy things at the Arctic circle, then take a train back to Helsinki. I would want to see Savonlinna's Olavinlinna Castle and visit the Saimaa region. I would love to hear what others would recommend for winter.





If it were just me, I would explore on my own and probably have a lot less things booked in advance as they will be infinitely cheaper than booking a sightseeing tour except the ferries and flights.