Thanks for bringing up Stenhammar, this is charming! The most often played piano piece by him here is the B minor fantasy, eg http://www.youtube.com/watch?v=keSoGQFHiqc
(sorry if I break a rule by posting a link, if so I'll remove it). It is apparently not as hard as it sounds (I never tried it). I does sound a bit like Brahms.
I'm not so sure about Swedish music being overly cheerful. Some folk music is but it is really dance music and is supposed to cheer people up. There is quite a wide spectrum. Sure we don't have a "defining" composer (unless you count Grieg, since Sweden and Norway were one country at the time) but I'm not sure that is a bad thing.
Chris, make sure you include Peterson-Berger in your list to try. In particular his suite Frösöblomster (flowers from Frösö) is charming and not too difficult. The piece "Sommarsång" in it is performed constantly at student recitals (at least that used to be the case when I attended such). Any Swedish pianist will know it, it almost has the same status as Fur Elise. Me, I never played either of them but I was kind of rebellious in some respects.
A Swedish favourite of mine is the Chaconne (op
by Gunnar de Frumerie, quite impressive but not too hard. A link where you can listen to some samples of his work is:http://www.prestoclassical.co.uk/w/1685 ... No-2-Op-65