This is a collation issue. The Swedish dictionary treats o-ring and o as distinct letters of the alphabet, whereas the international collation treats them as different variants of the same letter.
These queries should do the trick for you.
SELECT *
FROM g2_se_raw_zip
WHERE province COLLATE utf8_swedish_ci EQUALS 'Håbo'
SELECT *
FROM g2_se_raw_zip
WHERE province COLLATE utf8_swedish_ci = 'Håbo'
You may wish to change the collation setting of columns in your database containing Swedish place names to the Swedish collation for the sake of index performance. But, if you're developing a pan-European application you may prefer to ask users to tell you their own national language in their user profiles so you can search in a way that meets their expectations.