Many different versions of muumins have been produced in many different countries (even in the Soviet Union if I'm not mistaken) and it has been especially popular on Japan so no wonder theres an anime version of it too, but thats propably not the version you've seen as kids.
I beg to differ. Originally, the Moomin aired in Japan in the beginning of the 70s, and the show was vastly different from the ones produced twenty years later - so different, in fact, that Tove Jansson agreed it to be aired on the condition that it wouldn't be distributed outside Japan.
The newest Moomin series, the Japanese/Finnish version, aired in 1990 and was followed by a one-season sequel as well as a movie. This 're-make' is credited to be the one that sparked the popularity in Finland, Japan, and in other countries. According to wiki, no other series have been created in Japan since, so I think it's safe to assume that we watched the same series as the Japanese (with different dubs, of course) when we were children.
The slight difference in art Daggerlite mentioned might be just due the fact that the art of the original series changed in the last twenty chapters or so, making it slightly more 'anime-like'.
I heard [only rumors] that Japanese people thoughts that moomins were a real trolls who lives in Finnish forests. :S
*sigh* If only, if only...
