Magnetic domain structure and spin-dependent reflectivity measurements on cobalt thin films intercalated at the graphene/Ir(111) interface are investigated using spin-polarised low-energy electron microscopy. We find that graphene-covered cobalt films have surprising magnetic properties. Vectorial imaging of magnetic domains reveals an unusually gradual thickness-dependent spin reorientation transition, in which magnetisation rotates from out-of-the-film plane to the in-plane direction by less than 10° per cobalt monolayer. During this transition, cobalt films have a meandering spin texture, characterised by a complex, three-dimensional, wavy magnetisation pattern. In addition, spectroscopy measurements suggest that the electronic band structure of the unoccupied states is essentially spin-independent already a few electron-Volts above the vacuum level. These properties strikingly differ from those of pristine cobalt films and could open new prospects in surface magnetism.