Finland has the highest energy consumption per capita in EU. (over 2x Germany for example)
Winters are cold and we use electricity for heating a lot (gas furnaces at homes are very rare). Also bunch of energy hungry industry (paper, metal)
That's a kind of a blessing actually. As opposed to central Europe, Finland is not that dependent on gas from Russia. Electricity can be produced without a pipeline dependence on Russia.
That being said, Finland used to import quite a lot of electricity from Russia, and that is now gone, so there is an urgent need to invest in domestic production capacity. In the short term that certainly means much more wind, longer term hopefully more nuclear reactors (in addition to the soon upcoming OL3) coming online would be useful too.
According to Wikipedia:
DE: 232/km2
FI: 16.4/km2
EU: 106/km2
They should probably be OK as far as GP's argument is concerned (space for wind turbines not bothering anyone), especially since I expect most of the people are living in the south. Not sure whether there's enough wind in the sparsely populated areas, though.
But still we got our own NIMBYs who like to complain a lot.
edit: And the best places to build wind is at the coast so west and south parts of the country. It just is more windy at the coast and/or open sea pretty much always.
The absolute amount of capacity that has to come online for self-sufficiency would be a sliver of the demand of a more populous nation.