We report a novel, simple, versatile, and reproducible approach for the in situ synthesis of iron oxide nanoparticles (NP) on the surface of carbon nanotubes (CNT). Chemically functionalized single- or multi-wall CNT were used as nanotemplates for the synthesis of a range of very small (<10 nm) ferrimagnetic and/or anti-ferromagnetic iron oxide NP on their surface. For the synthesis of the hybrid materials, we employed for the first time a modified wet impregnation method involving the adsorption of ferric cations (as nanoparticle's precursor) on the functionalized nanotube surface and the subsequent interaction with acetic acid vapors followed by calcination at 400 degrees C under different atmospheres (air, argon, and oxygen). X-ray diffraction, transmission electron microscopy, Mossbauer spectroscopy, and magnetization measurements were used to study in-detail the morphology, size, and type of crystalline phases in the resulting hybrid materials. In addition, Raman measurements were used to monitor possible structural changes of the nanotubes during the synthetic approach. The experimental results were further supported by density functional theory calculations. These calculations were also used to disclose, how the type of the carbon nanotube template affects the nature and the size of the resulting NP in the final hybrids.