You need to define a locale that contains ä/ö/ü for \w to include them. You need to do this even for UTF-8. UTF-8 is just a standard way of representing characters, not the set of characters that can make up words in a particular language.

use locale;
use POSIX 'locale_h';
my $loc = 'de_DE.utf8';  # German locale, for example. Run 'locale -a'
+ to get the exact locale name
setlocale(LC_CTYPE, $loc)
  or die "Invalid locale $loc";
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Either that, or use this little trick off of my home node: [A-Za-zÀ-ÿœŒ] instead of \w :)

I probably should add that the German locale will likely not match 'ë', since it does not exist in German. Maybe Dutch or French...