I think there exists research on it, and in the context of CO2 equivalents per kilowatthour, wind power is one of the "greenest" there is. The CO2-cost of nuclear power is much higher, as far as I remember.

There are other environmental costs though ...

• The area directly by the wind mills are probably more or less "destroyed". Sometimes there are also access restrictions around windmill parks ... at least I've been sailing detours outside Copenhagen as a rather big area is closed due to windmills. How is it in the Norwegian mountains?
• Construction of access roads. I believe it's not a big deal if they are made as modest as possible and very rarely used (closed for other motorized traffic, that is).
• According to the Norwegian legal definition, a large area of "wilderness" is lost. However, I believe this is mostly a "statistical loss".
• Birdstrike is a big problem as far as I've understood it
• Noise
• Many people don't like them because they are ugly. However, I'd say that's mostly about aesthetics and not so much of an environmental cost. The wildlife most likely won't suffer due to the change of view.
• I remember to have read something in the news about a reindeer owner that was complaining loudly that the windmills was a direct threat against her way of living, as it would block the migration path of her reindeer (the only possible migration path). When reading the article, it was easy to sympathize with the lady, but now that I'm writing this I'm wondering why some few towers can be a real obstruction for reindeer.

So everything considered, windmills are probably one of the "greenest" source of power we have available today. However, it's required with a lot of windmills to sustain modern living, and while "some few" windmills probably can be said to be harmless wrg of the "destruction of nature"-argument, "a lot" of windmills probably can't be said to be harmless.

It's definitively better to have Teslas driving around in the city centers compared to dirty diesel cars, but it's no silver bullet. I do believe we need to consume less energy.