Not just barns, the stereotypical swedish red houses with white detailing exist pretty much because of a single copper mine in the town Falun, where they got so much leftover product to turn into paint that it basically supplied the entire country even to this day.

https://en.wikipedia.org/wiki/Falu_red

That town also spawned the equally stereotypical (though less internationally known) Falu sausage, which is probably one of the most popular meat products here.

https://en.wikipedia.org/wiki/Falukorv

And lastly to hammer home how insanely important this mine has been: It has been continously mined from like year 800 up until the 90's, has been the source of a lot of improvements to global mining technology, and as of 2001 it is a UNESCO world heritage site.
It's honestly kind of weird it's not more well known, and i HIGHLY recommend visiting the museum and going on a tour through the actual mine itself.

You can get there by train comfortably by taking the Snälltåget night train from hamburg (or even berlin) to stockholm and then the SJ intercity to Falun.

sure, lots and lots of Swedes came to the States in the 19th Century.. they tended to settle the Northern States and build farms, like everyone else was doing..

More than just Swedish barns. Red houses with white corners are a key part of a Swedish countryside

And norwegian fishing huts