Ok, I did it:
You can always switch between english and the language you downloaded Hearthstone in (if different from english) using the client.config in you Hearthstone directory. For example, I downloaded it in spanish so I can always change between enGB and esES in the file and it'll work flawlessly.
For any third language you will need additional files. Those files are contained in the archive base-Win-LANG.MPQ where LANG is your language (e.g. base-Win-ES.MPQ). But those files do not have any effect unless copied to Hearthstone/Data/Win. They are 2 files named soundslangLANG0.unity3d and spellslangLANG0.unity3d. Example of additional files I pasted in this directory: soundsdeDE0.unity3d and spellsdeDE0.unity3d.
"Where do I find additional language files?" Only from downloading the whole client to get hold of base-Win-LANG.MPQ or asking someone who has them on their drive. The archive itself is 37-39 MB, while the 2 extracted files are 40+ MB.
Extract the 2 files and copy them into Programs (x86)/Hearthsone/Data/Win. And do not forget to still edit client.config accordingly.
EDIT: I uploaded the soundfiles I had to Dropbox, so feel free to use them. They are already unzipped, so just paste them into the directory mentioned above. If anyone wants to upload the other soundfiles/MPQ then I'd be happy to link them here
Spanish and German files