The texture property is a SmartPointerProperty which cannot be saved/loaded.

I discussed this with Stefan who wanted to remove this property and make it a method of mitk::Surface.

There are two major possibilities:
1.Keep the current implementation as a property and implement reader/writer for this property. It is basically a vtkImageData plus some texture coordinates. The texture coordinates are already saved inside .vtp/.vtk surface files. vtkImageData could be saved as .nrrd (or other formats) using existing writers.

2.Move the property to methods of mitkSurface e.g.:
mitk::Surface::SetTextureCoordinates()
mitk::Surface::SetTexture()
This would allow the user to directly modify the basedata, as it might be expected, however, saving loading would also not be possible. The standard file formats for surfaces do not allow saving texture.

Both, Stefan and I, did not really need loading/saving of this "property" or functionality, but we agreed it would be nice to have.

Conclusion:
This is a "nice to have" feature request and there are different pro/con arguments if this should be a property or not.