In this paper, we exploit a large suite of ENZO cosmological magneto-hydrodynamical simulations adopting uniform mesh resolution, to investigate the properties of cosmic filaments under different baryonic physics and magnetogenesis scenarios. We exploit an isovolume-based algorithm to identify filaments and determine their attributes from the continuous distribution of gas mass density in the simulated volumes. The global (e.g. mass, size, mean temperature and magnetic field strength, and enclosed baryon fraction) and internal (e.g. density, temperature, velocity, and magnetic field profiles) properties of filaments in our volume are calculated across almost four orders of magnitude in mass. The inclusion of variations in non-gravitational physical processes (radiative cooling, star formation, feedback from star forming regions, and active galactic nuclei) as well as in the seeding scenarios for magnetic fields (early magnetization by primordial process versus later seeding by galaxies) allows us to study both the large-scale thermodynamics and the magnetic properties of the Warm-Hot Intergalactic Medium (WHIM) with an unprecedented detail. We show how the impact of non-gravitational physics on the global thermodynamical properties of filaments is modest, with the exception of the densest gas environment surrounding galaxies in filaments. Conversely, the magnetic properties of the WHIM in filament are found to dramatically vary as different seeding scenarios are considered. We study the correlation between the properties of galaxy-sized haloes and their host filaments, as well as between the haloes and the local WHIM in which they lie. Significant general statistical trends are reported.