One of the advantages of anisotropic soft materials is that their structures and, consequently, their properties can be controlled by moderate external fields. Whereas the control of materials with uniform orientational order is straightforward, manipulation of systems with complex orientational order is challenging. We show that a variety of structures of an interesting liquid material, which combine chiral orientational order with ferromagnetic one, can be controlled by a combination of small magnetic and electric fields. In the suspensions of magnetic nanoplatelets in chiral nematic liquid crystals, the platelet's magnetic moments orient along the orientation of the liquid crystal and, consequently, the material exhibits linear response to small magnetic fields. In the absence of external fields, orientations of the liquid crystal and magnetization have wound structure, which can be either homogeneously helical, disordered, or ordered in complex patterns, depending on the boundary condition at the surfaces and the history of the sample. We demonstrate that by using different combinations of small magnetic and electric fields, it is possible to control reversibly the formation of the structures in a layer of the material. In such a way, different periodic structures can be explored and some of them may be suitable for photonic applications. The material is also a convenient model system to study chiral magnetic structures, because it is a unique liquid analog of a solid helimagnet.