Okay, as stated in this comment, Telia appears to be the only Danish provider offering the textmessage-by-email feature for free, so... I did some browsing and some googling around on telia.dk, and found this FAQ page, which apparently says that 'e-mail textmessages' should be sent to firstname.lastname@example.org, with the x's being the number. Nothing about limits and such though. And since I'm using Orange, I'm not able to test this. :/
I tried putting my linguistic skills on a test with the Swedish page as well, but couldn't find anything of apparent interest there.