...because the error goes like this: The format of the chosen model isn't supported.

Which means that the file is either corrupted or not a DAE file at all (despite it's extension). It can also mean that the file contains a full scene which might prevent it from being imported. If you have Blender installed you can try to import the file in Blender (requires the Collada plugin). From Blender you can export to obj/mtl which is the default format that Sweet Home 3D uses.
You can also try this (or a similar) service to make sure that you have a valid file and while you're there you can let it convert to obj/mtl if you want.

You can try to import a model by dragging the zipped obj or dae file into the 2Dview pane. Make sure the level is visible. Windows or Linux users can import files without the necessity of being zipped but zipped files can be imported too.