It seems like certain Nordic cultures seem to have some similarities with Asian cultures. One example that should be mentioned is the common ancestry between the Finnish and Japanese languages to Altaic languages. This is however the only connection I can seem to find that is definite, other than that, I also found traditional Norwegian/Swedish architecture to resemble that of possibly Japanese/Chinese design.
To add to the similarities, it seems as though Norwegian and Swedish are tonal languages contrary to Finnish, could this also be a connection to China?
To add to what's already been said, you should really just forget about Alatic in this. It's not a real thing, at least as far as Macro-Altaic which is the grouping that includes Japanese. There's still some support for Micro-Altaic as a grouping, but this does not include Japanese or Korean.
Anything you find about Altaic that includes those two languages can be disregarded as rejected by the vast majority of linguists.
Also, tonality is something that can develop in languages which were previously not tonal, and tones can be lost in languages that were once tonal. /u/komnenos makes the point that Swedish is a pitch-accent language, but this doesn't matter. There are Chinese languages which are also pitch accent instead of being tonal in the sense that Mandarin is. But again since tonality is something that can easily show up or disappear in languages, it's a moot point. There's no value in using the presence tone as an analytical datapoint.
The Swedish, Norwegian, Danish and Icelandic are all Indo European languages and Mandarin is a Sino-Tibetan language. They have thousands of years of separate history between them.
Also, Norwegian and Swedish are pitch languages while Mandarin and many of the other Chinese dialects are tonal languages.
You could take a look at northern nomadic cultures, particularly herders, and even more particularly reindeer cultures. I don't know whether these do/did exist in Japan or Korea, but certainly northern China (e.g. Inner Mongolia), Mongolia, Siberia and some of the other former Soviet Republics like Tuva, across the arctic to the Sami people in Scandinavia -- and the nomadic cultures across the arctic in North America to Greenland, for that matter. So if you're looking for something that links them, that could be interesting, but I don't think that's really what you mean.