Infopath filler uses settings from client machine's operaing system (Windows), even if it is the same machine as sharepoint server set in Control Panel > Regional and Language Settings > Regional Optionstab > Standards and Formulas > Customize

while sharepoint (server), and I guess Infopath browser forms running by Sharepoint server 2010 Infopath Form Services, use sharepoint site's Regional settings < Site settings (under Site Administration section) < Site actions, on ribbon, in browser:

So, I would have tried to set Danish everywhere I could find.
Update:
Replied here the same but it seems did not work for others.
Please note that there are there are at least 4 places with regional settings possibly involved which are in:
- server's operating system
- sharepoint site
- Infopath formatting
- Client machine's operating systems, they are many