I would imagine that he cost of the heating fuels is pretty much the same all over Europe.
UK has 3.16 million hectares of woodland[1], Finland has 23 million hectares[2] of forest. UK population is 65 million, Finland has 5 million. [Wikipedia]
With 7 times more trees potentially providing fuel for 1/13th as many people, shouldn't it work out noticably cheaper?
I do not know, but if wood (or biomass) was noticeably cheaper than fossil fuels, I would think there was no need for climate agreements and there would be a large industry shipping wood from Canada and Siberia to use as a fuel.
Wikipedia says "The wood stove sauna is the most common type of sauna [in Finland] outside of the city areas".
In the context of "It's amazing if Finland has solved poverty to the level that every household can afford to set aside the space for a sauna and costs of running it.", and rural areas tend to be poorer than city areas, discussing wood as fuel for said saunas seems relevant.