Basically the parking is free. Santa Claus Village for sure is free (would be quite deserted if there was a fee).
There may be meterd areas, but if you are willing to walk a bit, parking is free. I've never paid a dime for parking.
Well, true and false. In downtown there are very fee totally free parking lots anymore (there are some next to the football stadium).
Most roadside parking is chargeable, BUT shopping malls and supermarkets offer free parking for the first two hours. It is disc parking. Shopping mall Sampokeskus is an exception. They have their own parking system and it is free for the first hour.
Parking charge is 1.40€ / hour and there is only one parking zone.
The church I can't remember, but Santa Claus Village is all free, as is the train station. Airport has it's own parking system also.
But roadside parking is free from Saturday afternoon until Monday morning.